MODELING AND CONTROL OF HYBRID WIND/PHOTOVOLTAIC/FUEL CELL DISTRIBUTED
Transcript of MODELING AND CONTROL OF HYBRID WIND/PHOTOVOLTAIC/FUEL CELL DISTRIBUTED
MODELING AND CONTROL OF HYBRID
WINDPHOTOVOLTAICFUEL CELL DISTRIBUTED GENERATION SYSTEMS
by
Caisheng Wang
A dissertation submitted in partial fulfillment of the requirement for the degree
of
Doctor of Philosophy in
Engineering
MONTANA STATE UNIVERSITY Bozeman Montana
July 2006
copyCOPYRIGHT
by
Caisheng Wang
2006
All Rights Reserved
ii
APPROVAL
of a dissertation submitted by
Caisheng Wang
This dissertation has been read by each member of the thesis committee and has been found to be satisfactory regarding content English usage format citations bibliographic style and consistency and is ready for submission to the Division of Graduate Education
Dr M Hashem Nehrir
Approved for the Department of Electrical and Computer Engineering
Dr James N Peterson
Approved for the Division of Graduate Education
Dr Joseph J Fedock
iii
STATEMENT OF PERMISSION TO USE In presenting this dissertation in partial fulfillment of the requirements for a doctoral degree at Montana State University I agree that the Library shall make it available to borrowers under rules of the Library I further agree that copying of this dissertation is allowable only for scholarly purposes consistent with ldquofair userdquo as prescribed in the US Copyright Law Requests for extensive copying or reproduction of this dissertation should be referred to ProQuest Information and Learning 300 North Zeeb Road Ann Arbor Michigan 48106 to whom I have granted ldquothe exclusive right to reproduce and distribute my dissertation in and from microform along with the non-exclusive right to reproduce and distribute my abstract in any format in whole or in partrdquo
Caisheng Wang July 2006
iv
ACKNOWLEDGEMENTS
I am grateful to acknowledge and thank all of those who assisted me in my graduate
program at Montana State University First I would like to thank Dr Hashem Nehrir my
academic advisor here at MSU His guidance support patience and personal time
throughout my years as a graduate student have been truly appreciated Special thanks are
given to my other graduate committee members Dr Steven Shaw Dr Don Pierre Dr
Hongwei Gao Dr Robert Gunderson and Dr Gary Bogar Special thanks also go to Dr
Hong Mao for his time and clarifying conversations on design and control of power
electronic devices Mr Sreedhar Gudarsquos help in the model developing for wind energy
conversion systems and Mr Marc Kepplerrsquos help in setting up the experimental circuit
for PEM fuel cell model validation are acknowledged Most importantly I would like to
thank my family and friends for their support throughout all the years
v
TABLE OF CONTENTS
LIST OF FIGURES xii
LIST OF TABLES xi
Abstract xii
1 INTRODUCTION 1
World Energy Demands 1
World and US Electricity Demands amp Generation 2 Conventional Thermal Electric Power Generation 6 Coal 6 Natural Gas 6 Oil 7
Nuclear Power 9 Hydroelectric Power 9
Why AlternativeRenewable Energy 10
Recent Progress in AlternativeRenewable Energy Technologies 14 Wind Energy 14 Photovoltaic Energy 16 Fuel Cells 18 Other Renewable Energy Sources 20 Distributed Generation Applications 23
Need for the Research 26
Scope of the Study 28
Organization of the Dissertation 28
REFERENCES 30
2 FUNDAMENTALS OF ALTERNATIVE ENERGY SYSTEMS 33
Energy Forms 33 Definition of Energy 33 Mechanical Energy 34 Chemical Energy 35 Electrical and Electromagnetic Energy 35 Thermal Energy 36 Nuclear Energy 37
Fundamentals of Thermodynamics 37 The First Law of Thermodynamics 37 The Heat Engine and Carnot Cycle 39 The Second Law of Thermodynamics 41
vi
TABLE OF CONTENTS - CONTINUED
Heat Transfer 42 Heat Transfer by Conduction 42 Heat Transfer by Convection 42 Heat Transfer by Radiation 43
Fundamentals of Electrochemical Processes 43 The Gibbs Free Energy 43 Energy Balance in Chemical Reactions 44 The Nernst Equation 47
Fundamentals of Alternative Energy Systems 48 Wind Energy System 49 Energy in Wind 49 Power Extracted from Wind 49 Tip Speed Ratio 51 Wind Energy Conversion System 52 Constant Speed and Variable Speed Wind Energy Conversion Systems 53 Wind Turbine Output Power vs Wind Speed 54
Photovoltaic Energy System 57 Fuel Cells 59 PEMFC 61 SOFC 63 MCFC 65
Electrolyzer 66
Summary 69
REFERENCES 70
3 MULTI-SOURCE ALTERNATIVE ENERGY DISTRIBUTED GENERATION SYSTEM 72
Introduction 72
AC Coupling vs DC Coupling 75
Stand-alone vs Grid-connected Systems 79
The Proposed System Configuration 79
System Unit Sizing 80
REFERENCES 85
4 COMPONENT MODELING FOR THE HYBRID ALTERNATIVE ENERGY SYSTEM 89
Dynamic Models and Model Validation for PEMFC 89 Introduction 89 Dynamic Model Development 91
vii
TABLE OF CONTENTS - CONTINUED
Gas Diffusion in the Electrodes 92 Material Conservation Equations 96 Fuel Cell Output Voltage 97 Double-Layer Charging Effect 101 Energy Balance of the Thermodynamics 102
Dynamic Model Built in MatlabSimulink 104 Equivalent Electrical Model in Pspice 105 Internal Potential E 106 Circuit for Activation Loss 107 Circuits for Ohmic and Concentration Voltage Drops 108 Equivalent Capacitor of Double-layer Charging Effect 109 Thermodynamic Block 109
Model Validation110 Experimental Setup 111 Steady-State Characteristics 113 Temperature Response115 Transient Performance116
Dynamic Models for SOFC118 Introduction118 Dynamic Model Development 119 Effective Partial Pressures 120 Material Conservation Equations 124 Fuel Cell Output Voltage 126 Energy Balance of the Thermodynamics 131 Dynamic SOFC Model Implementation 135
Model Responses under Constant Fuel Flow Operation 137 Steady-State Characteristics 137 Dynamic Response 140
Constant Fuel Utilization Operation 144 Steady-state Characteristics 145 Dynamic Responses 147
Wind Energy Conversion System 150 Introduction 150 System Configuration 151
Dynamic Model for Variable Speed Wind Turbine 152 Wind Turbine Characteristics 152 Pitch Angle Controller 155 Variable-speed Wind Turbine Model 157
Dynamic Model for SEIG 157 Steady-state Model 157 Self-excitation Process 160 Dynamic Model of SEIG in dq Representations 161
viii
Responses of the Model for the Variable Speed WECS 165 Wind Turbine Output Power Characteristic 165 Process of Self-excitation in SEIG 166 Model Responses under Wind Speed Changes 169
Solar Energy Conversion System 172 Modeling for PV CellModule 172 Light Current 173 Saturation Current 174 Calculation of α 174 Series Resistance 175 Thermal Model of PV 175
PV Model Development in MATLABSimulink 176 Model Performance 177 Temperature Effect on the Model Performance 179
Maximum Power Point Tracking Control 180 Current-Based Maximum Power Point Tracking 180 Control Scheme 182 Simulation Results 183
Electrolyzer 185 U-I Characteristic 185 Hydrogen Production Rate 186 Thermal Model 187 Electrolyzer Model Implementation in MATLABSimulink 189 Electrolyzer Model Performance 191
Power Electronic Interfacing Circuits 193 ACDC Rectifiers 193 Simplified Model for Controllable Rectifiers 197
DCDC Converters 200 Circuit Topologies 200 State-space Models Based on the State-space Averaging Technique 202 Averaged Models for DCDC Converters 205
DCAC Inverters 208 Circuit Topology 208 State-Space Model 208 dq Representation of the State-Space Model 212 Ideal Model for Three-phase VSI 214
Battery Model 217
Models for Accessories 218 Gas Compressor 218 High Pressure H2 Storage Tank 219 Gas Pressure Regulator 220
Summary 223
ix
TABLE OF CONTENTS - CONTINUED
REFERENCES 224
5 CONTROL OF GRID-CONNECTED FUEL CELL POWER GENERATION SYSTEMS 231
Introduction 231
System Description 232
Controller Designs for Power Electronic Devices 238 Controller Design for the Boost DCDC Converter 238 Controller Design for the 3-Phase VSI 241 Current Control Loop 241 Voltage Control Loop 245 Control of Power Flow 247 Overall Power Control System for the Inverter 249
Simulation Results 250 Desired P and Q Delivered to the Grid Heavy Loading 251 PEMFC DG 251 SOFC DG 254
Desired P Delivered to the Grid Q Consumed from the Grid Light Loading 256 PEMFC DG 256 SOFC DG 258
Load-Following Analysis 260 Fixed Grid Power 260 Fixed FC Power 261
Fault Analysis 263
Summary 266
REFERENCES 268
6 CONTROL OF STAND-ALONE FUEL CELL POWER GENERATION SYSTEMS 271
Introduction 271
System Description and Control Strategy 272 Load Mitigation Control 272 Battery ChargingDischarging Controller 276 Filter Design 277
Simulation Results 279 Load Transients 279 DC Load Transients 280 AC Load Transients 280
Load mitigation 282
x
TABLE OF CONTENTS - CONTINUED
PEMFC System 282 SOFC System 286
Battery ChargingDischarging 289
Summary 292
REFERENCES 293
7 CONTROL SCHEMES AND SIMULATION RESULTS FOR THE PROPOSED HYBRID WINDPVFC SYSTEM 295
Introduction 295
System Control Strategy 295 Overall Power Management Strategy 296 AC Bus Voltage Regulator 299 Electrolyzer Controller 300
Simulation Results under Different Scenarios 301 Winter Scenario 303 Weather Data 303 Simulation Results 305
Summer Scenario 314 Weather Data 314 Simulation Results 316
Summary 330
REFERENCES 331
8 OPTIMAL PLACEMENT OF DISTRIBUTED GENERATION SOURCES IN POWER SYSTEMS 332
Introduction 332
Optimal Placement of DG on a Radial Feeder 333 Theoretical Analysis 334 Procedure to Find the Optimal Location of DG on a Radial Feeder 336 Case Studies with Time Invariant Loads and DGs 338 Case Study with Time Varying Load and DG 340
Optimal Placement of DG in Networked Systems 341
Simulation Results 345 Radial Feeder with Time Invariant Loads and DG 346 Radial Feeder with Time Varying Loads and DG 348 Networked Systems 351
Summary 358
xi
TABLE OF CONTENTS - CONTINUED
REFERENCES 359
9 CONCLUSIONS 361
APPENDICES 364
APPENDIX A abc-dq0 TRANSFORMATION 365 abc-dq0 Transformation 366 dq0-abc Transformation 367
APPENDIX B SIMULATION DIAGRAMS OF THE HYBRID ENERGY SYSTEM 368
APPENDIX C MATLAB PROGRAMS FOR DG OPTIMAL PLACEMENT 373 DG Optimal Program for the IEEE 6-Bus system 374 DG Optimal Program for the IEEE 30-Bus system 375
xii
LIST OF FIGURES
Figure Page
11 World Energy Consumption 1970-2025 2
12 World and US Electricity Demands 1980-2025 4
13 World Electricity Generating Capacity 1980-2025 5
14 The world and US net electricity generation by type in 2002 5
15 Fuel shares of world electricity generation 2002-2025 8
16 US electricity generation by fuel types 8
17 World crude oil prices1978-2006 13
18 The world and the US wind power cumulative capacity 16
19 Cumulative Installed PV capacity in IEA PVPS countries 18
110 Cumulative installed FC units world-wide 1990-2005 19
21 Block diagram of an ideal heat engine 39
22 Carnot cycle (a) P-V (pressure-volume) diagram 40
(b) T-S (temperature-entropy) diagram 40
23 Theoretical rotor efficiency vs v0v ratio 51
24 Block diagram of a typical wind energy conversion system 52
25 Constant and variable speed wind energy conversion systems 55
26 Typical curves for a constant speed stall controlled (dotted)
and variable speed pitch controlled (solid) wind turbine 56
27 Schematic block diagram of a PV cell 58
28 PV Cell module and array 59
29 Schematic diagram of a PEMFC 61
210 V-I characteristic of a 500W PEMFC stack 62
211 Schematic diagram of a SOFC 63
212 V-I characteristic of a 5kW SOFC stack 64
213 Schematic diagram of a MCFC 65
214 Progress in generic performance of MCFCs on reformate gas and air 66
215 Schematic diagram of an alkaline electrolyzer 68
31 Hybrid energy system integration DC coupling 75
xiii
Figure Page
32 Hybrid energy system integration (a) PFAC coupling (b) HFAC coupling 76
33 System configuration of the proposed multi-source alternative
hybrid energy system (coupling inductors are not shown in the figure) 81
34 Hourly average demand of a typical residence
in the Pacific Northwest area 82
41 Schematic diagram of a PEMFC and voltage drops across it 93
42 Equivalent circuit of the double-layer charging effect inside a PEMFC 101
43 Diagram of building a dynamic model of PEMFC in SIMULINK 105
44 Diagram of building an electrical model of PEMFC in Pspice 106
45 Electrical circuit for internal potential E 107
46 Electrical circuit for activation loss 107
47 Electrical circuit for ohmic voltage drop 108
48 Electrical circuit for concentration voltage drop 109
49 Equivalent circuit of thermodynamic property inside PEMFC 110
410 Experimental configuration on the SR-12 PEMFC stack 112
411 V-I characteristics of SR-12 and models114
412 P-I characteristics of SR-12 and models 114
413 Temperature responses of the SR 12 stack and models 115
414 Transient responses of the models in short time range 117
415 Transient responses of the models in long time range 117
416 Schematic diagram of a solid oxide fuel cell 121
417 Equivalent electrical circuit of the double-layer charging effect inside a SOFC 130
418 Heat transfer inside a tubular solid oxide fuel cell 132
419 Diagram of building a dynamic model of SOFC in SIMULINK 137
420 V-I characteristics of the SOFC model at different temperatures 138
421 Three voltage drops at different temperatures 139
422 P-I characteristics of the SOFC model at different temperatures 140
423 Model dynamic responses with different equivalent
capacitance values for double-layer charging effect in small time scale 141
xiv
Figure Page
424 Model dynamic responses under different
operating pressures in medium time scale 142
425 Model dynamic responses under different
inlet temperatures in large time scale 143
426 Model temperature responses 144
427 Constant utilization control 145
428 V-I and P-I characteristics of the SOFC model
under constant fuel utilization and constant fuel flow operating modes 146
429 H2 input for the constant utilization and constant flow operating modes 147
430 Model dynamic responses under different operating pressures
in medium time scale with constant utilization operating mode 149
431 System block diagram of the WECS 152
432 Cp-λ characteristics at different pitch angles (θ) 154
433 Variable speed pitch controlled wind turbine operation regions 155
434 Pitch angle controller 156
435 Simulation model of the variable speed pitch-regulated wind turbine 156
436 Equivalent T circuit of self-excited induction generator with R-L Load 159
437 Determination of stable operation of SEIG 161
438 dq representation of a SEIG (All values are referred to stator) 162
439 Wind turbine output power characteristic 166
440 A successful self excitation process 167
441 Voltage fails to build up 167
442 Variation of magnetizing current Im 168
443 Variation of magnetizing inductance Lm 168
444 Wind speed variations used for simulation study 169
445 Output power of the WECS model under wind speed changes 169
446 Wind turbine rotor speed 170
447 Pitch angle controller response to the wind changes 171
448 Variation of power coefficient Cp 171
xv
Figure Page
449 One-diode equivalent circuit model for a PV cell
(a) Five parameters model (b) Simplified four parameters model 172
450 Block diagram of the PV model built in MATLABSimulink 176
451 I-U characteristic curves of the PV model under different irradiances 178
452 P-U characteristic curves of the PV model under different irradiances 178
453 I-U characteristic curves of the PV model under different temperatures 179
454 P-U characteristic curves of the PV model under different temperatures 179
455 Linear relationship between Isc and Imp under different solar irradiances 181
456 Ump vs Uoc curve under different solar irradiances 181
457 CMPPT control scheme 182
458 Imp and Ipv curves under the CMPPT control 183
459 PV output power and the maximum power curves 184
460 Block diagram of the electrolyzer model built in MATLABSimulink 189
461 U-I characteristics of the electrolyzer model under different temperatures 191
462 Temperature response of the model 192
463 Three-phase full diode bridge rectifier 194
464 Three-phase 12-diode bridge rectifier with a Y-Y and a Y-∆ transformer 195
465 A 6-pulse thyristor rectifier 197
466 Block diagram of the simplified model for 3-phase controllable rectifiers 198
467 DC output voltages of the different rectifier models 199
468 AC side phase current of the different rectifier models 199
469 Boost DCDC converter 201
470 Buck DCDC converter 201
471 Averaged model for boost DCDC converters 205
472 Simulation result of the averaged model for boost DCDC converter 206
473 Simulation result of the detailed model for boost DCDC converter 206
474 Averaged model for buck DCDC converters 207
475 Simulation result of the averaged model for buck DCDC converter 207
476 Simulation result of the detailed model for buck DCDC converter 208
xvi
Figure Page
477 3-phase DCAC voltage source inverter 209
478 Ideal model for three-phase VSI 215
479 AC phase output voltages of the ideal VSI model and the switched VSI model216
480 Output power of the ideal VSI model and the switched VSI model 216
481 Equivalent circuit model for battery reported in [481] 217
482 Simplified circuit model for lead-acid batteries 218
483 Pressured H2 storage tank 219
484 Gas pressure regulator 221
485 Performance of the model for gas pressure regulators 222
51 Block diagram of a fuel cell distributed generation system 233
52 Block diagram of the control loop for the boost DCDC converter 239
53 Bode plot of the control loop of the boost DCDC converter 240
54 Block diagram of the current control loop of the inverter 242
55 Bode plot of the current control loop 244
56 Unit step response of the current control loop and its approximation 245
57 Block diagram of the voltage control loop of the inverter 245
58 Bode plot of the voltage control loop 247
59 Power flow between a voltage source and utility grid 247
510 Block diagram of the overall power control system of the inverter 249
511 PEMFC DG P and Q delivered to the grid under heavy loading 252
512 PEMFC DG dq values of the inverter output voltage under heavy load 252
513 PEMFC DG Output voltage and current of
each fuel cell array under heavy load 253
514 PEMFC DG DC bus voltage waveform under heavy load 254
515 SOFC DG P and Q delivered to the grid under heavy loading 254
516 SOFC DG Output voltage and current of each FC array under heavy load 255
517 SOFC DG DC bus voltage under heavy loading 255
518 PEMFC DG P and Q delivered to the grid light loading 257
519 PEMFC DG Output voltage and current of
xvii
Figure Page
each fuel cell array under light loading 257
520 SOFC DG P and Q delivered to the grid under light loading 259
521 SOFC DG Output voltage and current of each fuel cell array under light load 259
522 System for the PEMFC DG load-following study 261
523 Power curves of the load-following study with fixed grid power 262
524 System for the PEMFC DG load-following study 262
525 Power curves of the load-following study with fixed FC power 263
526 Faulted fuel cell DG system 264
527 Faulted PEMFC DG Power flow of the transmission line 265
528 Faulted PEMFC DG Fuel cell output powers for the fault studies 266
61 Schematic diagram of a FC-battery hybrid system
with load transient mitigation control 274
62 Schematic diagram of the battery chargingdischarging controller 275
63 Example of the responses of different filters to a load transient 278
64 Load transient of starting a 25HP and a 5kW 220V DC motor 280
65 AC load transient used on PEMFC-battery system 282
66 Reference signal (Iref) for the current controller battery current (ib)
and converter output current (idd_out) under the load transient for
PEMFC shown in Figure 64 284
67 The PEMFC output current and voltage responses to the
DC load transient shown in Figure 64 284
68 PEMFC The control reference signal (Iref) and battery current (ib)
under the AC load transient shown in Figure 65 285
69 The PEMFC output current and voltage responses
to the AC load transient shown in Figure 65 286
610 Reference signal (Iref) for the current controller the battery current (ib)
and the converter output current (idd_out) under the load transient
for SOFC shown in Figure 64 287
611 SOFC output current and voltage responses
xviii
Figure Page
to the DC load transient shown in Figure 64 287
612 Control reference signal (Iref) and battery current (ib)
under the AC load transient 288
613 The SOFC output current and voltage responses to the AC load transient 288
614 Battery voltage and extra current reference (Iref2) curves
when the battery is being charged 290
615 The load transient the overall current control reference signal (Iref)
the low-pass filter output signal (Iref1) and the corresponding
converter output current (idd_out) when the battery is being charged 291
71 Simulation model for the proposed
hybrid alternative energy system in MATLABSimulink 297
72 Block diagram of the overall control scheme for
the proposed hybrid alternative energy system 298
73 Block diagram of the AC voltage regulator 299
74 Block diagram of the electrolyzer controller 300
75 Load demand profile over 24 hours for the system simulation study 302
76 Wind speed data for the winter scenario simulation study 303
77 Solar irradiance data for the winter scenario simulation study 304
78 Air temperature data for the winter scenario simulation study 304
79 Wind power of the winter scenario study 305
710 Pitch angle of the wind turbine of the winter scenario study 306
711 Rotor speed of the induction generator of the winter scenario study 306
712 PV power for the winter scenario 308
713 Current difference between the actual output current and
the reference current for the maximum power point of the winter scenario 308
714 The PV temperature response over the simulation period for
the winter scenario 309
715 Power available for H2 generation of the winter scenario 309
716 H2 generation rate of the winter scenario study 310
xix
Figure Page
717 Electrolyzer voltage and current for the winter scenario study 310
718 Power shortage over the simulation period of the winter scenario study 311
719 Power supplied by the FC of the winter scenario study 312
720 H2 consumption rate of the winter scenario study 312
721 The pressure tank over the 24 hour of the winter scenario study 313
722 The battery power over the simulation period for the winter scenario 314
723 Corrected wind speed data for the summer scenario simulation study 315
724 Irradiance data for the summer scenario simulation study 315
725 Air temperature data for the summer scenario simulation study 316
726 Wind power generated for the summer scenario study 317
727 Rotor speed of the induction generator for the summer scenario study 317
728 PV power generated for the winter scenario study 318
729 The PV and air temperature over the simulation period for
the winter scenario study 319
730 Power available for H2 generation for the summer scenario study 320
731 H2 generation rate for the summer scenario study 320
732 Electrolyzer voltage and current for the summer scenario study 321
733 Power shortage over the simulation period for the summer scenario study 322
734 Power supplied by the FC over the simulation period for
the summer scenario study 322
735 H2 consumption rate for the summer scenario study 323
736 The H2 tank pressure over the 24 hour for the summer scenario study 323
737 The battery power over the simulation period for the summer scenario 324
738 Wind speed data for the simulation study with continuous
weather data and load demand 325
739 Solar irradiance data for the simulation study with
continuous weather data and load demand 325
740 Air temperature for the simulation study with
continuous weather data and load demand 326
xx
Figure Page
741 Wind power for the continuous weather data and load demand scenario 327
742 PV power for the continuous weather data and load demand scenario 327
743 Power available for H2 generation for the
continuous weather data and load demand scenario 328
744 FC output power for the continuous weather data and load demand scenario 328
745 Battery power for the continuous weather data and load demand scenario 329
81 A feeder with distributed loads along the line 334
82 Procedure for finding optimal place for a DG source in a radial feeder 338
83 A networked power system 342
84 Flow chart of The theoretical procedure to find the
optimal bus to place DG in a networked system 346
85 A radial feeder with uniformly distributed loads 347
86 Annual daily average output power profile of a 1-MW wind-DG 349
87 Daily average demand of a typical house 350
88 Power losses of the radial feeder with the wind-DG at different buses 350
89 6-bus networked power system studied 351
810 Power losses of the system in Figure 89 with a 5MW DG 352
811 Values of the objective function of the system in Figure 89 353
812 IEEE 30-bus test system 354
813 Power losses of the IEEE 30-bus test system with a 15MW DG 354
814 Values of the objective function of the IEEE 30-bus system 355
815 Power losses of the subset system in Figure 812 with a 5MW DG 356
816 Values of the objective function of the subset system in Figure 812 356
B1 Simulink model for the wind energy conversion system 369
B2 Simulink model for the solar energy conversion system 370
B3 Simulink model for the fuel cell and the gas pressure regulation system 371
B4 Simulink model for the electrolyzer and the gas compression system 372
xi
LIST OF TABLES
Table Page 11 Current Status and the DOE Targets for
PEMFC Stack in Stationary Applications 21
12 Current status and the SECA targets for 3-10 kW
SOFC module in stationary applications 22
13 Technologies for Distributed Generation Systems 25
21 Standard thermodynamic properties (enthalpy entropy and Gibbs energy) 46
31 Comparison among Different Integration Schemes 78
32 Component Parameters of the Proposed Hybrid Energy System 84
41 Analogies between Thermodynamic and Electrical Quantities 110
42 Specifications of SR-12 111
43 Electrical Model Parameter Values for SR-12 Stack 112
44 Operating Conditions for the Model Dynamic Response Studies 141
45 Parameter values for C1-C5 153
46 SEIG Model Parameters 165
47 The PV Model Parameters 177
48 The Electrolyzer Model Parameters 190
49 Constants of Beattie-Bridgeman Equation of State for H2 220
51 Configuration Parameters of the Proposed System 236
52 System Parameters of the Boost DCDC Converter 240
53 Parameters of the Current Control Loop the Inverter 243
54 Parameters of the Voltage Control Loop the Inverter 246
61 Parameters of the DCDC Converter 275
62 Parameters of the Battery Model 276
71 Weather Station information at
Deer Lodge Montana AgriMet Station (DRLM) 302
81 Theoretical Analysis Results of Case Studies
with Time Invariant Loads and DGs 339
82 Parameters of the System in Figure 85 347
xii
83 Simulation Results of Case Studies with Time Invariant Loads and DG 348
84 Parameters of the System in Figure 89 352
85 Bus Data of the IEEE 30-Bus Test System 357
xii
Abstract
Due to ever increasing energy consumption rising public awareness of environmental protection and steady progress in power deregulation alternative (ie renewable and fuel cell based) distributed generation (DG) systems have attracted increased interest Wind and photovoltaic (PV) power generation are two of the most promising renewable energy technologies Fuel cell (FC) systems also show great potential in DG applications of the future due to their fast technology development and many merits they have such as high efficiency zero or low emission (of pollutant gases) and flexible modular structure
The modeling and control of a hybrid windPVFC DG system is addressed in this
dissertation Different energy sources in the system are integrated through an AC bus Dynamic models for the main system components namely wind energy conversion system (WECS) PV energy conversion system (PVECS) fuel cell electrolyzer power electronic interfacing circuits battery hydrogen storage tank gas compressor and gas pressure regulator are developed Two types of fuel cells have been modeled in this dissertation proton exchange membrane fuel cell (PEMFC) and solid oxide fuel cell (SOFC) Power control of a grid-connected FC system as well as load mitigation control of a stand-alone FC system are investigated The pitch angle control for WECS the maximum power point tracking (MPPT) control for PVECS and the control for electrolyzer and power electronic devices are also addressed in the dissertation
Based on the dynamic component models a simulation model for the proposed hybrid
energy system has been developed using MATLABSimulink The overall power management strategy for coordinating the power flows among the different energy sources is presented in the dissertation Simulation studies have been carried out to verify the system performance under different scenarios using a practical load profile and real weather data The results show that the overall power management strategy is effective and the power flows among the different energy sources and the load demand is balanced successfully
The DGrsquos impacts on the existing power system are also investigated in this
dissertation Analytical methods for finding optimal sites to deploy DG sources in power systems are presented and verified with simulation studies
1
CHAPTER 1
INTRODUCTION
Energy is essential to everyonersquos life no matter when and where they are This is
especially true in this new century where people keep pursuing higher quality of life
Among different types of energy electric energy is one of the most important that people
need everyday In this chapter an overview is given on the world energy demand
electricity consumption and their development trend in the near future The electric power
generation technologies based on different energy sources are also reviewed in the
chapter Finally the need for this research work is addressed and the scope of the research
is also defined
World Energy Demands
The world energy consumption is expected to grow about 57 in the next two
decades [11] Figure 11 shows the strong growth of the global energy demand in the
past three decades and its projection over the next two decades The world energy
consumption by fuel type in 2002 is also shown in the figure It is clear that a large part
of the total energy is provided by fossil fuels (about 86 in 2002) The future of the
global economy growth is highly dependent on whether the ever-increasing energy
demand can be met
Fossil fuels are not evenly distributed around the world and regional or global
conflicts may arise from energy crisis if our economy is still heavily dependent on them
Moreover during the process of generating and using electrical energy with todayrsquos
2
conventional technologies the global environment has already been significantly affected
and the environment of some regions has been damaged severely Therefore it is a big
challenge for the whole world to figure out how to generate the needed amount of energy
and the types of energy sources
207243
285310
348366
412
504
553
598
645
0
100
200
300
400
500
600
700
800
1970 1975 1980 1985 1990 1995 2002 2010 2015 2020 2025
Quadrillion Btu
History Projections Nuclear
7
Other
8
Coal
24
Oil
38
Natural
Gas
23
Figure 11 World Energy Consumption 1970-2025 [11]-[13]
World and US Electricity Demands amp Generation
The world electric energy consumption is expected to increase by more than 50 by
2025 [11]-[13] shown in Figure 12 About 24 of the world total electricity demand in
2003 is consumed by US (Figure 12) and it is anticipated to grow 44 in the first
quarter of the new century [11]-[13] Moreover the electricity demand from emerging
economic regions such as China and India is increasing even faster
3
To meet the future global electricity demand an extensive expansion of installed
generating capacity is necessary Worldwide installed electricity generating capacity is
expected to increase from 3626 GW (gigawatts) in 2003 to 5495 GW in 2025 (Figure
13) at a 22-percent average annual growth rate [11]-[14]
The percentage of US electricity generating capacity over the total world generating
capacity is declining It drops from around 25 in 2003 to about 20 in 2025 (Figure 13)
according to the estimation of Energy Information Administration (EIA) Nevertheless
the electricity generation capacity of US is still expected to grow about 38 from 2000
to 2025 [11] By comparing the electricity consumption data in Figure 12 and the
generation capacity data in Figure 13 it is noted that the US electricity consumption is
growing faster than the generation capacity If this trend is not reversed it is expected
that the US would have to import more electric power in the near future Otherwise the
reserve margin of the whole power system in the US will shrink which will
compromise system stability and power delivery reliability
Electricity can be generated in many ways from various energy sources Electric
power can be generated by conventional thermal power plants (using fossil fuels or
nuclear energy) hydropower stations and other alternative power generating units (such
as wind turbine generators photovoltaic arrays fuel cells biomass power plants
geothermal power stations etc) Fossil fuels (including coal oil and natural gas) and
nuclear energy are not renewable and their resources are limited On the other hand
renewable energy resources (wind and solar energy for example) can self-renew and
sustain for future use Figure 14 shows the world and US net electricity generation by
type in 2002 It is clear from this figure that more than 80 of the world and US
4
electricity generation are still contributed by the conventional fossil-fuel thermal power
plants and nuclear power plants [11] [14] Except for the hydroelectric power the
portion of the electricity generated from other renewablealternative sources is very small
In the following of this section an overview will be given on the current status and the
future development trend of different types of electricity generation
0
5000
10000
15000
20000
25000
30000
1980 1985 1990 1995 2000 2002 2003 2010 2015 2020 2025
World
US
Billion kWh
History Projections
Figure 12 World and US Electricity Demands 1980-2025 [11]-[13]
5
0
1000
2000
3000
4000
5000
6000
1980 1985 1990 1995 2000 2003 2010 2015 2020 2025
World
US
GW
History Projections
Figure 13 World Electricity Generating Capacity 1980-2025 [11] [14]
Nuclear
17
Hydroelectric
17 Conventional
Thermal
64
Hydroelectric
7
Nuclear
20
Conventional
Thermal
71
Figure 14 The world and US net electricity generation by type in 2002 [11] [14]
6
Conventional Thermal Electric Power Generation
Conventional thermal power plants generate electric power using fossil fuels namely
coal oil and natural gas In a fossil-fired thermal power plant water passes through a
boiler heated by burning fossil fuels to produce high temperature and high pressure
steam The steam then enters a multi-stage steam turbine which operates a generator to
produce electricity
Coal Due to its low price and relative abundant reserves coal is and should
continue to be the dominant fuel for electricity generation of the world and the US
shown in Figures 15 and 16 The United States and China currently are the leaders in
terms of installed coal-fired capacity Both countries have large amount of coal reserves
Even under the pressure of Kyoto Protocol for reducing greenhouse gas and other air
pollutant emissions coal-fired electricity generation capacity is still expected to grow by
15 percent per year and coal is expected to fuel 38 (Figure 15) of the electricity
generation of the entire world by 2025 [13] However this trend could be changed if
higher pressure is applied to implement environment protection policies such as the
Kyoto Protocol and the Clean Air Act in the US
Natural Gas Natural-gas-fired power generation technology is an attractive option
for new power plants because of its fuel efficiency operating flexibility rapid
deployment and lower installation costs compared to other conventional generation
technologies Regulatory policies to reduce carbon dioxide emissions could accelerate the
switch from coal to gas However the amount of natural gas reserve is not as plentiful as
7
coal In the US the amount of dry natural gas reverses was 192513 billion cubic feet in
2004 [14] In the same year the total natural gas consumption in the US was 224303
billion cubic feet And about a quarter of this consumption was for electricity generation
If dry natural gas was the only means of reserving and the amount of reserves would not
change then that amount could only supply the US natural gas needs for less than 10
years at the consumption rate of 2004 [14]
Oil On the world average oil is not and will not be a major source for electric
power The main reason is that the major petroleum products are produced for
transportation purposes such as automobile gasoline jet fuel etc but not for electricity
generation The first problem with oil is that the whole world is short of its reserves while
the demand for oil keeps increasing The oil demand is expected to grow at about 25
per year [15] The amount of proven crude oil reserves in the world in 2005 is 1277
billion barrels1 The world oil consumption in 2002 was 782 million barrels per day [15]
If we could keep this consuming rate unchanged then the whole world oil reserves could
only sustain for less than 45 years Even if the more optimistic data 2947 billion barrels
(including reserve growth and the estimated undiscovered oil reserves) of the oil reserves
are used the world will still run out of oil in about one hundred years and forty years
under the same consumption rate Greenhouse gas and air pollutant emission is another
big problem with using oil Moreover there are many other problems associated with oil
such as high oil price and the instability of some oil production regions
1 1 barrel = 42 US gallons
8
0
20
40
60
80
100
120
2002 2010 2015 2020 2025
HydroelectricOther
Nuclear
Natural Gas
Oil
Coal
Percentage
Figure 15 Fuel shares of world electricity generation 2002-2025 [11] [12]
0
500
1000
1500
2000
2500
3000
3500
4000
4500
5000
1990 2000 2010
HydroelectricOther
Nuclear
Natural Gas
Oil
Coal
Billion kWh
Figure 16 US electricity generation by fuel types [14]
9
Nuclear Power
Nuclear energy is an important source for electricity generation in many countries In
2003 19 countries depended on nuclear power for at least 20 percent of their electricity
generation [16] France is the country which has the highest portion (781) of the
electricity generated by nuclear power [16] Though the percentage of nuclear electric
power over the total national electricity generation is not very high (about 20) the US
is still the worlds largest producer of electric power using nuclear fuels Higher fossil
fuel prices and the entry into force of the Kyoto Protocol could result in more electricity
generated by nuclear power In the emerging economic regions such as China and India
nuclear power capacity is expected to grow [11] However nuclear power trends can be
difficult or even be reversed due to a variety of reasons The safety of a nuclear power
plant is still the biggest concern And how to deposit nuclear wastes can always be a
discussion topic for environmentalists Moreover the nuclear fuel (Uranium) is not
renewable The US Uranium reserves are 1414 million pounds at the end of 2003 [16]
This amount of reserve can supply the US for about 270 years at the Uranium annual
consumption rate of 24072 metric tons (2002 statistical data)
Hydroelectric Power
Today hydropower is still the largest renewable source for electricity generation in
the world In 2002 more than 18 of the world electricity was supplied by renewable
sources most of which comes from hydropower shown in Figure 15 [11] [12] The
world hydroelectric capacity is expected to grow slightly due to large hydroelectric
projects in the regions with emerging economies The Three Gorges hydropower project
10
in China is now the biggest hydropower project ever carried out in the world Upon the
completion of the Three Gorges project in 2009 it will have a generating capacity of 182
GW (26 units total and 700MW for each unit) [17]
Although the hydropower is clean and renewable there are still some problems
associated with it First the big dams and reservoirs cause a lot of environmental
concerns and social disputes Second the relocation of reservoir populations can be a big
problem For example over a million people will be relocated for the Three Gorges
project [18] Moreover hydropower is not as abundant as desired In the US for
example the available hydropower sources (except in Alaska) have almost been explored
All these factors determine that hydropower can not play a major role in the future new
electricity supply in the world
Why AlternativeRenewable Energy
The term ldquoalternative energyrdquo is referred to the energy produced in an
environmentally friendly way (different from conventional means ie through fossil-fuel
power plants nuclear power plants and hydropower plants) Alternative energy
considered in this dissertation is either renewable or with high energy conversion
efficiency There is a broad range of energy sources that can be classified as alternative
energy such as solar wind hydrogen (fuel cell) biomass and geothermal energy
Nevertheless as mentioned in the previous section at the present the majority of the
world electricity is still generated by fossil fuels nuclear power and hydropower
However due to the following problemsconcerns for conventional energy technologies
the renewablealternative energy sources will play important roles in electricity
11
generation And sooner or later todayrsquos alternatives will become tomorrowrsquos main
sources for electricity
1) Conventional energy sources are not renewable As discussed in the above
section both the fossil fuels (coal and oil and natural gas) and nuclear fuels are not
renewable The reserves of these fuels will run out some day in the future A long term
energy development strategy is therefore important for sustainable and continuous
economy growth
2) Conventional generation technologies are not environmentally friendly
Although there have been substantial improvements in the technologies (such as
desulfurization) for reducing emissions conventional thermal power plants still produce a
large amount of pollutant gases such as sulfur oxide and nitrogen oxide [19] The
radioactive waste of nuclear power plants is always a big concern to the environment
The dams and reservoirs of hydropower can change the ecological systems of the original
rivers and the regions of the reservoirs substantially [110]
3) The cost of using fossil and nuclear fuels will go higher and higher Since these
fuel sources are not renewable while the world energy demand is steadily increasing it is
obvious that the price of these fuels will go higher Taking world crude oil price for
example the price has been increased by 57 in the last year [111] Compared to natural
gas and petroleum coal is cheap for electricity generation However if the cost for
reducing emissions is taken into account the actual price of generating electricity from
coal would be much higher The growing cost of using conventional technologies will
make alternative power generation more competitive and will justify the switchover from
conventional to alternative ways for electric power generation
12
4) Hydropower sources are not enough and the sites are normally far away from
load centers Hydropower is good because it is clean and renewable However as
mentioned in the previous section the total amount of hydropower that can be explored is
not enough And in many developed countries the hydropower has been almost explored
fully Moreover hydroelectric sites normally are in remote areas Long transmission lines
add more difficulties and cost in exploring hydropower since the permission of the
right-of-way for transmission lines is much more difficult to obtain than before
5) Political and social concerns on safety are pushing nuclear power away In
general government energy strategy guides the development of nuclear power There are
almost no cases that corporations or utilities make the decisions to build nuclear power
plants based on their economic considerations Accidents at the Three Mile Island nuclear
power plant in the United States in 1979 and Chernobyl in the Soviet Union in 1986 fed
people full of fears No body wants to be a neighbor of a nuclear power plant or facility
This changes the government energy policy substantially In the US there is no new
order for nuclear units in the near future [16] In Europe several countries including
Italy Austria Belgium Germany and Sweden stepped out from nuclear power even
before the Chernobyl disaster [11]
On the other hand compared with conventional electricity generation technologies
alternativerenewable power have the following advantages
1) Renewable energy resources are not only renewable but also abundant For
example according to the data of 2000 the US wind resources can produce more
electricity than the entire nation would use [112] The total solar energy from sun in a
day at the earth surface is about 1000 times more than the all fossil fuels consumption
13
[19]
0
10
20
30
40
50
60
1978
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
US $ per barrel
Figure 17 World crude oil prices1978-2006 [111]
(Note The price is based on the first week data of January in each year)
2) Fuel cell systems have high energy efficiency The efficiency of low temperature
proton exchange membrane (PEM) fuel cells is around 35-45 [113] High temperature
solid oxide fuel cells (SOFC) can have efficiency as high as 65 [114] The overall
efficiency of an SOFC based combined-cycle system can even reach 70 [114]
3) Renewable energy and fuel cell systems are environmentally friendly From these
systems there is zero or low emission (of pollutant gases) that cause acid rain urban
smog and other health problems and therefore there is no environmental cleanup or
waste disposal cost associated with them [19]
4) Different renewable energy sources can complement each other Though renewable
14
energy resources are not evenly distributed throughout the world every region has some
kinds of renewable energy resources At least sunlight reaches every corner in the world
And different energy resources (such as solar and wind energy) can complement each
other This is important to improve energy security for a nation like the US which is
currently dependent on the foreign energy sources
5) These renewablealternative power generation systems normally have modular
structure and can be installed close to load centers as distributed generation sources
(except large wind and PV farms) Therefore no high voltage transmission lines are
needed for them to supply electricity
In general due to the ever increasing energy consumption the rising public
awareness for environmental protection the exhausting density of fossil-fuel and the
intensive political and social concerns upon the nuclear power safety alternative (ie
renewable and fuel cell based) power generation systems have attracted increased
interest
Recent Progress in AlternativeRenewable Energy Technologies
In the following section the recent progress in wind power solar power fuel cells
and other renewable energy technologies will be reviewed An overview on their
applications as distributed generation will also be given
Wind Energy
Wind energy is one of worlds fastest-growing energy technologies Both the global
and US wind energy experienced a record year in 2005 According to the figures
15
released by the Global Wind Energy Council (GWEC) in 2005 there was a 434
increase in annual additions to the global market and a 5642 increase in the annual
addition to the US wind power generation capacity Last year was just one of the record
years In the past 11 years the global wind energy capacity has increased more than 17
times mdash from 35 GW in 1994 to almost 60 GW by the end of 2005 (Figure 18) In the
United States wind power capacity has increased more than 3 times in only 5 years (from
2554 MW in 2000 to 9149 MW by the end of 2005) also shown in Figure 18 The future
prospects of the global wind industry are also very promising even based on a
conservative projection that the total global wind power installed could reach 160 GW by
2012 A spread of new countries across the world will participate in the global wind
energy market in the next ten years [115]
The phenomenal worldwide growth of the wind industry during the past decade can
be attributed to supportive government policies and the fast development in innovative
cost-reducing technologies In the US the work conducted under the Wind Energy
Programrsquos Next Generation Wind Turbine (1994 ndash 2003) and WindPACT (1999 ndash 2004)
projects under the Department of Energy (DOE) resulted in innovative designs high
power ratings and increased efficiencies [116] All these technological advances have
led to dramatic reductions in cost of electricity (COE) mdash from $08kWh in the
early1980s to about $004kWh today for utility-scale (normally gt= 750kW) turbines
[116] [19] Although this drop in COE has been impressive more research work is still
needed to make wind power more competitive Development in aerodynamic efficiency
structural strength of wind turbine blades larger turbine blades and higher towers
variable speed generators and power controllers will help to reduce the COE further The
16
DOE goal is to reduce the COE produced by land-based utility-scale turbines located in
Class 4 wind resource areas (areas with 58 ms wind speed at a10-m height) to
$003kWh by 2012 [116]
0
10000
20000
30000
40000
50000
60000
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005
World
US
MW
Figure 18 The world and the US wind power cumulative capacity [115] [116]
Photovoltaic Energy
Solar energy basically is the ultimate source for all kinds of energy resources on the
earth with only a few exceptions such as geothermal energy There are normally two
ways to generate electricity from sunlight through photovoltaic (PV) and solar thermal
systems In this section and this dissertation only photovoltaic energy and system will be
discussed
Just like the growth of wind energy PV energy is another fast growing renewable
energy technology Though the absolute size of global solar power generation capacity is
17
much smaller than wind power it has been increased even faster than wind power during
the past dozen years (from 1992-2004) [117] In terms of the market for PV power
applications in the IEA-PVPS2 (International Energy Agency ndash Photovoltaic Power
Systems Programme) countries the total installed PV capacity has been increased more
than 23 times ndash from the 110 MW in 1992 to 2596 MW in 2004 (Figure 19) [117]
Due to improvements in semiconductor materials device designs and product quality
and the expansion of production capacity capital costs for PV panels have been
decreased significantly from more than $50W in the early of 1980s [19] to about 35$ to
45$ per watt in 2004 [117] The cost of electricity produced by PV systems continues to
drop It has declined from $090kWh in 1980 to about 020$kWh today [19] In the
US the DOE goal is to reduce the COE of PV to $006kWh by 2020 [119] However
PV energy is still usually more expensive than energy from the local utility Currently the
initial investment of a PV system is also higher than that of an engine generator
Nevertheless there are many applications for which a PV system is the most
cost-effective long-term option especially in remote areas such as power for remote
telecommunications remote lighting and signs remote homes and recreational vehicles
2 There are 19 countries participating in the IEA PVPS program They are Australia Austria Canada Denmark France Germany Israel Italy Japan Korea Mexico the Netherlands Norway Portugal Spain Sweden Switzerland UK and USA Over 90 of the world total PV capacity is installed in the IEA-PVPS countries The top three PV countries Japan Germany and the US are all the members of the organization
18
0
500
1000
1500
2000
2500
3000
1992 1994 1996 1998 2000 2002 2004
MW
Figure 19 Cumulative Installed PV capacity in IEA PVPS countries [117]
Fuel Cells
Fuel cells (FCs) are static energy conversion devices that convert the chemical energy
of fuel directly into DC electrical energy Fuel cells have a wide variety of potential
applications including micro-power auxiliary power transportation power stationary
power for buildings and other distributed generation applications and central power
Since entering the new century fuel cell technologies have experienced exponential
growth shown in Figure 110 [120] The total number of fuel cell applications reached
14500 in 2005 [120] Government policies public opinion and technology advance in
fuel cells all contributed to this phenomenal growth
19
Figure 110 Cumulative installed FC units world-wide 1990-2005 [120]
Among different types of fuel cells polymer electrolyte membrane fuel cells
(PEMFC) and solid oxide fuel cells (SOFC) both show great potentials in transportation
and DG applications3 [113] [120] Compared with conventional power plants these
fuel cell DG systems have many advantages such as high efficiency zero or low emission
(of pollutant gases) and flexible modular structure Fuel cell DGs can be strategically
placed at any site in a power system (normally at the distribution level) for grid
reinforcement deferring or eliminating the need for system upgrades and improving
system integrity reliability and efficiency Moreover as a byproduct high-temperature
fuel cells also generate heat that makes them suitable for residential commercial or
industrial applications where electricity and heat are needed simultaneously [113]
[121]
3 Vehicle application is still the main market for PEMFC though it also has high potential for stationary power generation For SOFCs stationary power generation is their main application But they do have a foothold in the transport market as well with new planar design
20
The DOE recently updated its ldquoHydrogen Fuel Cells and Infrastructure Technologies
Programrsquos Multi-Year Research Development and Demonstration Planrdquo written in 2003
[122] In the Plan it lays out industry targets for key fuel cell performance indices such
as cost durability and power density In 1999 the Solid State Energy Conversion
Alliance (SECA) was founded for bringing together government industry and the
scientific community to promote the development of SOFC Through these years
collaborative work among the government industry national labs and universities great
advances in fuel cell technologies have been achieved in many aspects These address
FCs a bright future although extensive work is still needed to be done before they can
really play main roles in energy market Table 11 gives the current status and the DOE
goals for PEMFC [122] [123] Table 12 summaries the current development stage of
SOFC and SECA targets [124]-[126] It is noted from the two tables that the possibility
of reaching the ultimate DOE and SECA goals is high
Other Renewable Energy Sources
In addition to PV and wind energy there are many other renewable energy resources
such as biomass geothermal energy solar thermal energy and tidal power These energy
resources can all be utilized to generate electricity Among them biomass and geothermal
energy technologies have the leading generation capacity in the US [19]
21
TABLE 11 CURRENT STATUS AND THE DOE TARGETS A FOR
PEMFC STACK B IN STATIONARY APPLICATIONS
Characteristics Units Current Status
2010 Goal
Stack power density WL 1330 2000
Stack specific power Wkg 1260 2000
Stack efficiency 25 of rated power 65 65
Stack efficiency rated power 55 55
Precious metal loading gkW 13 03
Cost $kWe 75 30
Durability with cycling hours 2200 C 5000
Transient response (time for 10 to 90 of rated power)
sec 1 1
Cold startup time to 90 of rated power ndash20 ordmC ambient temperature
sec 100 C 30
Survivability ordmC -40 -40
A Based on the technical targets reported in [122] for 80-kWe (net) transportation
fuel cell stacks operating on direct Hydrogen
B Excludes hydrogen storage and fuel cell ancillaries thermal water air
management systems
C Based on the performance data reported by Ballard in 2005 [123]
Biomass can be burned directly co-fired with coal or gasified first and then used to
generate electricity It can also be used to generate bio-fuels such as ethanol Most of
todayrsquos US biomass power plants use direct-combustion method In 2004 the total
22
generation capacity of biomass reached 9709 MW about 1 of the total US electric
capacity [127]
TABLE 12 CURRENT STATUS AND THE SECA TARGETS FOR
3-10 KW SOFC MODULE IN STATIONARY APPLICATIONS
Phase I A Current Status II
III (By 2010)
Cost 800$kW 724$kW B $400kW
Efficiency 35-55 41 b 40-60 40-60
Steady State
Test Hours 1500 1500 1500 1500
Availability 80 90 B 85 95
Power Degradation per 500 hours
le2 13 C le1 le01
Transient Test
Cycles 10 na 50 100
Power Degradation after Cycle Test
le1 na le05 le01
Power Density 03Wcm2 0575Wcm2 D 06Wcm2 06Wcm2
Operating Temperature
800 ordmC 700-750 ordmC C 700 ordmC 700 ordmC
Evaluate the potential to achieve $400kW [124]
A The goals of Phase I have been achieved GE is the first of six SECA industry
teams to complete phase I of the program [125]
B Based on the data reported by GE
C Based on the data reported by FuelCell Energy [126]
D Based on the data reported by Delphi [125]
23
Geothermal energy can be converted into electricity by three technologies dry steam
flush and binary cycle The most common type of geothermal plants is flush power plant
while the world largest geothermal plant is of the dry steam type [128] The dry stream
geothermal power plant at The Geysers in California is the largest geothermal power
plant in the world with a capacity of 2000 MW [19] However due to the limited
amount of available geothermal heat resources one will not expect to see any
considerable growth in this area Actually the geothermal generation capacity in the US
declined from 2793MW in 2000 to 2133 MW in 2004 [127] Nevertheless it can be an
important energy source in remote areas where geothermal resources are available and
abundant
Distributed Generation Applications
The ever-increasing need for electrical power generation steady progress in the
power deregulation and utility restructuring and tight constraints over the construction of
new transmission lines for long distance power transmission have created increased
interest in distributed power generation DG sources are normally placed close to
consumption centers and are added mostly at the distribution level They are relatively
small in size (relative to the power capacity of the system in which they are placed and
normally less than 10 MW) and modular in structure These DG devices can be
strategically placed in power systems for grid reinforcement reducing power losses and
on-peak operating costs improving voltage profiles and load factors deferring or
eliminating the need for system upgrades and improving system integrity reliability and
efficiency [133]
24
The technology advances in renewable energy sources fuel cells and small generation
techniques provide a diverse portfolio for DG applications Table 13 shows the candidate
technologies for DG systems The DOE proposed a strategic plan for distributed energy
sources in 2000 [129] The energy market with DG sources in 2020 was envisioned in
the plan as ldquoThe United States will have the cleanest and most efficient and reliable
energy system in the world by maximizing the use of affordable distributed energy
resourcesrdquo [129] To achieve this ultimate goal the DOE also set sub-goals for DG
development The long-term goal by 2020 is ldquoto make the nationrsquos energy generation and
delivery system the cleanest and most efficient reliable and affordable in the world by
maximizing the use of cost efficient distributed energy resourcesrdquo The mid-term by 2010
is to reduce costs to increase the efficiency and reliability of distributed generation
technologies and to add 20 of new electric capacity By the end of 1999 about 22GW
distributed energy systems with 18 GW backup units were installed across the US [131]
According to EIA US generation capacity history and forecast data 198 GW of new
capacity is needed during the period between 2000 and 2010 [14] Based on the
mid-term goal 20 (396 GW) of the new addition should come from DG systems This
means about 44 annual growth rate in DG capacity
25
TABLE 13 TECHNOLOGIES FOR DISTRIBUTED GENERATION SYSTEMS [130]
Technology Size Fuel Electrical Efficiency
( LHV)
Combustion Turbine Combined Cycle
50-500 MW Natural gas liquid
fuels 50-60
Industrial Combustion Turbine
1-50 MW Natural gas liquid
fuels 25-40
Internal Combustion Turbine(Reciprocating
Engine)
1kW ndash 10 MW
Natural gas diesel oil propane gasoline etc
25-38
Mircroturbine 27-400 kW Landfill gas
propane natural gas and other fuels
22-30
Stirling Engine 11-50kW Any 18-25
Fuel Cells 1kW Natural gas H2
other H2-rich fuels 35-60
Photovoltaic 1W ndash 10MW Renewable 5-15 A
Wind Turbine 02kW ndash 5MW
Renewable lt 40
Biomass B Several kW ndash 20 MW
Renewable ~ 20
A PV cell energy conversion efficiency
B Based on the data reported in [19]
26
Need for the Research
The ever increasing energy consumption rapid progress in wind PV and fuel cell
power generation technologies and the rising public awareness for environmental
protection have turned alternative energy and distributed generation as promising
research areas Due to natural intermittent properties of wind and solar irradiation
stand-alone windPV renewable energy systems normally require energy storage devices
or some other generation sources to form a hybrid system Because some of renewable
energy sources can complement each other (section 13) multi-source alternative energy
systems (with proper control) have great potential to provide higher quality and more
reliable power to customers than a system based on a single resource However the
issues on optimal system configuration proper power electronic interfaces and power
management among different energy sources are not resolved yet Therefore more
research work is needed on new alternative energy systems and their corresponding
control strategies
Fuel cells are good energy sources to provide reliable power at steady state but they
cannot respond to electrical load transients as fast as desired This problem is mainly due
to their slow internal electrochemical and thermodynamic responses [132] The transient
properties of fuel cells need to be studied and analyzed under different situations such as
electrical faults on the fuel cell terminals motor starting and electric vehicle starting and
acceleration Therefore dynamic fuel cell models are needed to study those transient
phenomena and to develop controllers to solve or mitigate the problem
27
Fuel cells normally work along with power electronic devices One problem is that
there is not adequate information exchange between fuel cell manufacturers and power
electronic interface designers Without adequate knowledge about the area of each other
the fuel cell manufacturers normally model the power electronic interface as an
equivalent impedance while the power electronic circuit designers take the fuel cell as a
constant voltage source with some series resistance These inaccurate approaches may
cause undesired results when fuel cells and their power electronic interfaces are
connected together It is important and necessary to get a better understanding of the
impact of power electronic interface on fuel cellrsquos performance and of the fuel cellrsquos
impact on power electronic interfacing circuits Dynamic model development for fuel
cells using electrical circuits can be a solution so that the researchers in both areas can
understand each other Moreover it will provide a more efficient way to integrate the fuel
cells and power electronic devices together
Distributed generation devices can pose both positive and negative impacts on the
existing power systems [133] These new issues have led DG operation to be an
important research area Research on optimal placement (including size) of DGs can help
obtain maximum potential benefits from DGs
28
Scope of the Study
Although there are many types of alternativerenewable resources the alternative
sources in this dissertation are confined to wind PV and fuel cells for the research on the
proposed hybrid alternative energy systems The main focus is given to modeling
validation and control for fuel cells and fuel cell based stand-alone and grid-connected
systems Two types of fuel cells will be modeled and used in the dissertation PEMFC
and SOFC The ultimate goal of this dissertation is to model a multi-source alternative
DG system consisting of wind turbine(s) PV arrays fuel cells and electrolyzers and to
manage the power flows among the different energy resources in the system The optimal
placement of DG sources in power systems is also investigated on system operation level
Organization of the Dissertation
After the introduction conducted and the reason for the research explained in this
chapter Chapter 2 reviews the fundamentals of electrochemistry thermodynamics power
electronics and the alternative energy technologies including wind PV and fuel cells
Chapter 3 introduces hybrid energy systems gives possible ways of system integration
and presents a proposed hybrid windPVFC energy system Chapter 4 describes the
models for the components in the proposed system discussed in Chapter 3 Power
electronic interfacing circuits with appropriate controllers are discussed in Chapter 4 as
well
29
Chapters 5 and 6 focus on control for fuel cell based systems Control for
grid-connected fuel cell systems is discussed in Chapter 5 In Chapter 6 load mitigation
control for stand-alone fuel cell systems is investigated
The overall control scheme development for the proposed multi-source alternative
system is given in Chapter 7 Simulation results under different scenarios are given and
discussed in the chapter The optimal placement of DG sources in power systems (both
radial feeders and networked systems) is investigated in Chapter 8
30
REFERENCES
[11] International Energy Outlook 2005 Energy Information Administration (EIA) httpwwweiadoegoviea
[12] International Energy Annual 2003 EIA httpwwweiadoegoviea
[13] System for the Analysis of Global Energy Markets 2005 EIA httpwwweiadoegoviea
[14] Annual Energy Outlook 2006 (Early Release) EIA httpwwweiadoegov
[15] World Oil Market International Energy outlook - International Petroleum (Oil) Reserves and Resources EIA httpwwweiadoegoviea
[16] US Nuclear Generation of Electricity EIA httpwwweiadoegoviea
[17] Online http www3ggovcn
[18] Million Relocates of Unprecedented Scale httpwww3ggovcnshuniuymgc200305170065htm
[19] SR Bull ldquoRenewable Energy Today and Tomorrowrdquo Proceedings of IEEE Vol 89 No 8 pp1216-1221 August 2001
[110] FA Farret and MG Simotildees Integration of Alternative Sources of Energy John Wiley amp Sons Inc 2006
[111] World Crude Oil Prices EIA httptontoeiadoegovdnavpetpet_pri_wco_k_whtm
[112] M R Patel Wind and Solar Power Systems CRC Press LLC 1999
[113] Fuel Cell Handbook (Sixth Edition) EGampG Services Inc Science Applications International Corporation DOE Office of Fossil Energy National Energy Technology Lab Nov 2002
[114] O Yamamoto ldquoSolid oxide fuel cells fundamental aspects and prospectsrdquo Electrochimica Acta Vol 45 No (15-16) pp 2423-2435 2000
[115] Global Power Source Global Wind Energy Council httpwwwgwecnet
[116] Wind Power Today ndash Federal Wind Program Highlights NREL DOEGO-102005-2115 April 2005
31
[117] Trends in photovoltaic applications Survey report of selected IEA countries between 1992 and 2004 International Energy Agency Photovoltaics Power Systems Programme (IEA PVPS) September 2005
[118] Online httpwwwnrelgovanalysisnewsletters2006_januaryhtml
[119] National Status Report 2004 ndashUSA IEA-PVPS httpwwwoja-servicesnliea-pvpsnsr04usa2htm
[120] Fuel Cell Today 2005 Worldwide Survey httpwwwfuelcelltodaycom
[121] James Larminie and Andrew Dicks Fuel Cell Systems Explained 2nd Edition John Wiley amp Sons Ltd 2003
[122] The Hydrogen Fuel Cells amp Infrastructure Technologies Program Multi-Year Research Development and Demonstration Plan February 2005 Version
[123] Technology Road Map ndashBallard Power Systems Inc httpwwwballardcombe_informedfuel_cell_technologyroadmap
[124] SECA Program Plan DOE Office of Fossil Energy The DOE National Energy Technology Laboratory (NETL) and the Pacific Northwest National Laboratory Jan 2002
[125] Significant Milestone Achieved in SECA Fuel Cell Development Program httpwwwnetldoegovpublicationsTechNewstn_ge_secahtml Jan 2006
[126] Thermally Integrated High Power Density SOFC Generator FuelCell Energy Inc FY 2004 Progress Report
[127] Renewables and Alternate Fuels Energy Information Administration (EIA) httpwwweiadoegovfuelrenewablehtml
[128] Online httpwwweereenergygovgeothermalpowerplantshtmlflashsteam
[129] Strategic Plan for Distributed Energy Resources mdash Office of Energy Efficiency and Renewable Energy US Department of Energy September 2000
[130] DER Technologies Electric Power Research Institute (EPRI) October 2002
[131] Establishing a Goal for Distributed Energy Resources Distributed Energy Resources The Power to Choose on November 28 2001 by Paul Lemar httpwwwdistributed-generationcomLibrarypaul_lemarpdf
[132] C Wang MH Nehrir and SR Shaw ldquoDynamic Models and Model Validation for PEM Fuel Cells Using Electrical Circuitsrdquo IEEE Transactions on Energy Conversion vol 20 no 2 pp442-451 June 2005
32
[133] C Wang and MH Nehrir ldquoAnalytical Approaches for Optimal Placement of Distributed Generation Sources in Power Systemsrdquo IEEE Transactions on Power Systems vol 19 no 4 pp 2068-2076 Nov 2004
33
CHAPTER 2
FUNDAMENTALS OF ALTERNATIVE ENERGY SYSTEMS
This chapter reviews the fundamental concepts and principles of energy systems and
energy conversion The overview of the fundamentals of electrochemistry
thermodynamics and alternative energy systems is a good introduction for understanding
and modeling of the proposed multi-source alternative energy system discussed in the
following chapters
Energy Forms
Definition of Energy
Energy is defined as the amount of work a physical system is capable of doing
Energy is a fundamental quantity that every physical system possesses In a broad sense
energy can neither be created nor consumed or destroyed However it may be converted
or transferred from one form to other Generally speaking there are two fundamental
types of energy transitional energy and stored energy [21] Transitional energy is energy
in motion also called kinetic energy such as mechanical kinetic energy Stored energy is
energy that exists as mass position in a force field (such as gravity and electromagnetic
fields) etc which is also called potential energy More specifically energy can exist in
the following five basic forms
(1) Mechanical energy
(2) Chemical energy
(3) Electrical and electromagnetic energy
34
(4) Thermal energy
(5) Nuclear energy
Mechanical Energy
Mechanical energy is the type of energy associated with moving objects or objects
that have potential to move themselves or others It can be defined as work used to raise a
weight [21] The mechanical kinetic energy of a translating object (Emt) with a mass m at
speed v is
2
2
1mvEmt = (21)
For a rotating body with moment of inertia (rotational inertia) I at angular speed ω its
kinetic mechanical energy (Emr) is defined as
2
2
1ωIEmr = (22)
Mechanical potential energy is the energy that a given system possesses as a result of
its status in a mechanical force field [21] For example in a gravity field g the potential
mechanical energy of a body with mass m at height h is given as
mghEmpg = (23)
As another example the potential energy of an elastic spring with the spring constant
k at the displacement x is
2
2
1kxEmps = (24)
35
Chemical Energy
Chemical energy is the energy held in the chemical bonds between atoms and
molecules [22] Every bond has a certain amount of energy Chemical energy exists as a
stored energy form which can be converted to other energy forms through reactions First
energy is required to break the bonds - called endothermic Then energy will be released
(called exothermic) when these broken bonds combine together to create more stable
molecules If the total energy released is more than the energy taken in then the whole
reaction is called exothermic Otherwise the reaction is called endothermic The burning
of fossil fuels (combustion) is one of the most important exothermic reactions for
producing energy Photosynthesis is a good example for endothermic reaction since
plants use energy from sun to make the reaction happen
Electrical and Electromagnetic Energy
Electrical and electromagnetic energy is the energy associated with electrical
magnetic andor electromagnetic fields It is normally expressed in terms of electrical
andor electromagnetic parameters For example the electro-static energy stored in a
capacitor is
C
qEC
2
2
1= (25)
where C is the capacitance of the capacitor and q is the total charge stored
The magnetic energy stored in an inductor with inductance L at current i is
2
2
1LiEm = (26)
36
Another expression used to represent magnetic energy is [23]
int=V
m dVHE 2
2
1micro (27)
where micro is the material permeability H is the magnetic field intensity and V is the object
volume under consideration This expression is especially useful in calculating hysteresis
losses inside power transformers
Radiation energy is one of the forms of electromagnetic energy The radiation energy
only exists in transitional form and it is given by [21]
fhER sdot= (28)
where h is the Planckrsquos constant (6626times10-34 Js) and f is the frequency of the radiation
Thermal Energy
From a macroscopic observation thermal energy or heat can be defined as energy
transferred between two systems due to temperature difference [24] From a micro-level
point of view thermal energy is associated with atomic and molecular vibration [21] All
other forms of energy can be converted into thermal energy while the opposite conversion
is limited by the second law of thermodynamics (which will be explained briefly in
section 22) Based on this fact thermal energy can be considered the most basic form of
energy [21]
37
Nuclear Energy
Nuclear energy is a topic irrelevant to this dissertation But for the completion of the
discussion on energy forms a very brief overview on nuclear energy is also included here
Similar to chemical energy nuclear energy is also a type of stored energy The energy
will be released as a result of nuclear reaction (normally fission reaction) to produce a
more stable configuration Take the uranium-235 nucleus as an example When it
captures a neutron it will split into two lighter atoms and throws off two or three new
neutrons The new atoms then emit gamma radiation as they settle into their new more
stable states An incredible amount of energy is released in the form of heat and gamma
radiation during the above process The mass of fission products and the neutrons
together is less than the original U-235 atom mass The mass defect is governed by the
famous Einsteinrsquos mass-energy equation [21]
E = mc2 (29)
where m is the material mass and c is the speed of light in vacuum (asymp2998times108 ms)
Fundamentals of Thermodynamics
Thermodynamic analysis of energy conversion processes is important for modeling
and control of hybrid energy systems Therefore in this section a brief overview of the
fundamental concepts and principles of thermodynamics is given
The First Law of Thermodynamics
According to the first law of thermodynamics the energy of a system is conserved
Energy here is in the form of either of heat or work This law describes that energy can
38
neither be created or destroyed but it can be converted from one type to another The
change in the system energy dE is contributed by the heat entering (dQ) the system and
the work done by the system (dW) to the outside [25] [26]
dWdQdE minus= (210)
Note that the work in the above equation is the work leaving the system The system
here is an idealized object which is used to limit our study scope A system can be
isolated from ldquoeverything elserdquo in the sense that changes in everything else need not
affect its state [25] The external ldquoeverything elserdquo is considered to be the environment
of the system Of particular interest is one type of system called a simple system that is
not affected by capillarity distortion of solid phase external force fields (electromagnetic
and gravitational) or internal adiabatic walls [25] For a simple system the total system
energy is equal to the total system internal energy denoted by symbol U [25] In this
dissertation we only consider simple systems
E = U (211)
For a control volume or open system (any prescribed and identifiable volume in
space) usually there is expansion when heat is absorbed by the system at constant
pressure Part of the heat goes into internal energy and causes temperature to rise And the
rest of the heat is used to expand against the pressure P A property of the system called
enthalpy (H) is used to represent the system state under certain condition
H = U +PV (212)
where V is the system volume Enthalpy is a state parameter which is independent of
which way the system reaches that condition Equation (211) now can be represented as
39
dWdQdH minus= (213)
The Heat Engine and Carnot Cycle
The heat engine is designed to convert heat to work Figure 21 shows the block
diagram of an idealized heat engine If we want the heat engine to work continuously
then the system (the working substance in the figure) is subjected to a cyclic process A
cyclic process is one in which the system returns to its original state after a cycle For a
practical heat engine there are many processes undergoing And it is also complicated
and difficult to analyze all of them In 1842 a French scientist named Sadi Carnot
presented a way to analyze cyclic thermal processes and discovered the maximum
possible heat efficiency of a heat engine
Figure 21 Block diagram of an ideal heat engine
The Carnot cycle is shown in Figure 22 The cycle consists of two isothermal
processes and two adiabatic processes Figure 22 (a) shows the P-V diagram of the
40
Carnot cycle [26] The heat Q1 enters the system at T1 and Q2 leaves system at T2 Since
this process is cyclic the system energy remains the same after any cycle According to
the First Law of Thermodynamics (Equation 210) it can be shown that
S∆
(a) (b)
Figure 22 Carnot cycle (a) P-V (pressure-volume) diagram (b) T-S (temperature-entropy) diagram
21 QQW minus= (214)
W is the work done by the system to the outside which can also be represented by the
area abcd in Figure 22 (a) For the Carnot cycle it has been proved that
2
2
1
1
T
Q
T
Q= (215)
The efficiency of the system then is
1
2
1
21
1
1T
T
Q
Q
Wc minus=
minus==η (216)
It is clear from (216) that in order to get a higher efficiency the temperature
difference should be larger
Another contribution from Carnot is that QT can be a state property of the system by
41
showing the equivalence of Q1T1 and Q2T2 [see (215)] Based on Carnotrsquos idea
Clausius developed the concept of entropy and presented the Second Law of
Thermodynamics
The Second Law of Thermodynamics
The concept is introduced to indicate to what extent of disorder a system is at If the
system is undergoing an infinitesimal reversible process with dQ heat entering the system
at temperature T then the infinitesimal change in its entropy is defined as [25]-[28]
revT
dQdS = (217)
A reversible process is a process that can be reversed without leaving any traces to its
environment If a cyclic process only consists of reversible processes then there is no
entropy change (∆S = 0) after a cycle On the other hand if the cycle contains an
irreversible process then a change of entropy will be generated Entropy is an important
system property It is also very useful in describing a thermodynamic process Figure 22
(b) shows the T-S diagram of a Carnot Cycle The area abcd also represents the work
done to the system environment
The Second Law of Thermodynamics is described by the Clausius inequality [25]
[28] For any cyclic process we have
int le 0T
dQ (218)
The equality sign only applies to a reversible cyclic process The above inequality can
be expressed in an infinitesimal form as
42
T
dQdS ge (219)
The equality sign applies to a reversible cyclic process and the inequality sign applies
to an irreversible process That is to say for any irreversible process it occurs in a
direction to which the change of entropy is greater than dQT This means that heat
cannot be transferred from a low temperature to a higher temperature without a need of
work from outside The Second Law also reveals that no real heat engine efficiency can
reach 100 due to the increase of entropy For an isolated system the change of entropy
will always be greater than or equal to zero
Heat Transfer
In this section the equations governing different ways of heat transfer are reviewed
Heat Transfer by Conduction For isotropic solids (whose properties and
constitution in the neighborhood of any two points are the same at any direction) heat
transfer by conduction is governed by Fourier heat-conduction equation [24]
d
TTkAQcond
12 minus= (220)
where Qcond is the heat transferred A is the face area of the element normal to the heat
flow k is the effective thermal conductivity d is the distance between the two points of
interest and (T2-T1) is the temperature difference
Heat Transfer by Convection Heat transfer by convection is the heat exchange
between a flowing fluid (natural or forced) and a solid surface The convective heat
transfer is given as [24]
43
)( sfconv TThAQ minus= (221)
where h is the effective convection heat transfer coefficient A is the solid area contacting
the fluid Tf is the bulk temperature of the fluid and Ts is the temperature of the solid This
equation is also called Newtonrsquos law of cooling
Heat Transfer by Radiation Based on (28) the radiation heat exchange rate
between two objects at different temperatures is [24]
)( 4
2
4
1 TTAQrad minus= εσamp (222)
where Qrad is the radiation heat (J) ε is the effective emissivity of the system σ is
Stefan-Boltzmann Constant (56703times10-8 Wmiddotm-2middotK-4)
Fundamentals of Electrochemical Processes
The Gibbs Free Energy
The Gibbs Free Energy also called the Gibbs Energy or ldquofree enthalpyrdquo is defined as
[25] [28]
G = H-TS = U + PV -TS (223)
Chemical reactions proceed towards the direction that minimizes the Gibbs Energy
Differentiating the above equation we can obtain
)()( SdTTdSVdPPdVdUSdTTdSdHdG +minus++=+minus= (224)
dG is negative as a chemical reaction approaches its equilibrium point and it will be
zero at the equilibrium point According to the First Law of Thermodynamics (210) for
a simple system the above equation can be rewritten as
)()( SdTTdSVdPPdVdWdQSdTTdSdHdG +minus++minus=+minus= (225)
44
If the system is restricted to performing only expansion-type of work (dW = PdV) and
the process is reversible (dQ = TdS) then four terms on the right side of (225) will be
cancelled out resulting in
SdTVdPdG minus= (226)
At a given temperature T Gibbs energy under any pressure can be calculated based
on the above equation for that given temperature
)ln()()(0
0
P
PnRTTGTG += (227)
where )(0 TG is the standard (P0 = 1 atm) Gibbs energy at temperature T
For an electrochemical reaction the maximum work (electricity) is determined by the
change in the Gibbs Energy as the reactants change to products It can be shown that the
maximum work is equal to the change in the Gibbs energy [28]
GWe ∆minus= (228)
Energy Balance in Chemical Reactions
In a chemical reaction the change in enthalpy due to the reaction is [28]
sumsum minus=minus=∆Rj
RjRj
Pi
PiPiRP HNHNHHH (229)
where HP is the total enthalpy of the products and HR is the total enthalpy of the reactants
NPi is the amount of moles of the ith species in the products and NRj is the amount of
moles of the jth species in the reactants Accordingly HPi (HRj) is the molar enthalpy of
the corresponding species which can be represented as
PifPi HHHH )( 00 minus+= (230)
45
where 0
fH is the standard molar enthalpy of formation (Jmol) and (H-H0) is the sensible
enthalpy due to the temperature difference
The change of entropy due to the reaction is [28]
sumsum minus=minus=∆Rj
RjRj
Pi
PiPiRP SNSNSSS (231)
where SP is the total entropy of the products and SR is the total entropy of the reactants
SPi (SRj) is the molar entropy of the corresponding species
The change of the Gibbs free energy due to the reaction then can be obtained from
(223) as
STHGGG RP ∆minus∆=∆minus∆=∆ (232)
Two example reactions [(233) and (234)] are given to show how to calculate the
change of Gibbs energy in a reaction The enthalpy and entropy values for water
hydrogen and oxygen are given in Table 21 The reactions are assumed to happen under
standard conditions (1 atm and 25 ˚C)
)(2
1222 gOHOH =+ (233)
)(2
1222 lOHOH =+ (234)
where subscript ldquogrdquo represents that the reaction product is in gas form and subscript
ldquolrdquo is used to indicate that the reaction product is in liquid form
46
TABLE 21 STANDARD THERMODYNAMIC PROPERTIES
(ENTHALPY ENTROPY AND GIBBS ENERGY) [29]
Name Hf (kJmol) S (JmolK)
H2O(g) -2418 1887
H2O(l) -2858 699
H2 0 1306
O2 0 205
For the reaction given in (233) we have
8241)008241( minus=minusminusminus=minus=∆ RP HHH (kJmol)
444)2055061307188( minus=timesminusminus=minus=∆ RP SSS (JmolK)
Therefore the change in the Gibbs energy of the reaction given in (233) is
=timesminustimesminusminus=∆minus∆=∆ minus )10444(2988241 3STHG -22857 kJmol
For the reaction given in (234) we have
8285)008285( minus=minusminusminus=minus=∆ RP HHH (kJmol)
2163)205506130969( minus=timesminusminus=minus=∆ RP SSS (JmolK)
Therefore the change in the Gibbs energy of the reaction given in (234) is
=timesminustimesminusminus=∆minus∆=∆ minus )102163(2988285 3STHG -23716 kJmol
From the above examples we can see that more work can be done if the product
(H2O) is in liquid form
47
The Nernst Equation
Consider an electrochemical reaction under constant temperature and pressure that the
reactants X and Y form products M and N given by (235)
dNcMbYaX +hArr+ (235)
where a b c and d are stoichiometric coefficients
According to (232) the change of the Gibbs energy of the reaction is [28]
YXNMRP bGaGdGcGGGG minusminus+=minus=∆
In terms of the change of the standard Gibbs energy G∆ can also be expressed as
[see (227)]
+∆=∆
b
Y
a
X
d
N
c
M
PP
PPRTGG ln0 (236)
where 00000
YXNM bGaGdGcGG minusminus+=∆
In an electrochemical reaction the work can be considered as the electrical energy
delivered by the reaction The electrochemical work is
FEnW ee = (237)
where ne is number of participating electrons F is Faraday constant (96487 Cmol) and E
is the voltage difference across the electrodes
According to (228) the change in Gibbs energy is the negative value of the work
done by the reaction
FEnWG ee minus=minus=∆ (238)
Under standard condition the above equation turns out to be
48
000 FEnWG ee minus=minus=∆ (239)
where E0 is the standard reference potential
From (238) we can calculate the electrode voltage E as
minus
∆minus=
∆minus=
b
Y
a
X
d
N
C
M
eee PP
PP
Fn
RT
Fn
G
Fn
GE ln
0
(240)
Writing the above in terms of standard reference potential E0 we get the well-known
electrochemical formula Nernst equation [28] [210]
+=
minus=
d
N
C
M
b
Y
a
X
e
b
Y
a
X
d
N
C
M
e PP
PP
Fn
RTE
PP
PP
Fn
RTEE lnln 00
(241)
For a fuel cell with an overall reaction as given by (233) then the voltage across the
fuel cell electrodes (or the internal potential of the fuel cell) is
+=
OH
OH
P
PP
F
RTEE
2
50
220 ln2
(242)
If the product (H2O) is in liquid form given by (234) then the fuel cell internal
potential is
( )5022
0 ln2
OH PPF
RTEE += (243)
Fundamentals of Alternative Energy Systems
In this section the fundamentals of wind energy generation system PV cells fuel
cells and electrolyzers are reviewed
49
Wind Energy System
Energy in Wind Wind energy systems harness the kinetic energy of wind and
convert it into electrical energy or use it to do other work such as pump water grind
grains etc The kinetic energy of air of mass m moving at speed v can be expressed as
[211]
2
2
1mvEk = (244)
During a time period t the mass (m) of air passing through a given area A at speed v
is
Avtm ρ= (245)
where ρ is the density of air (kgm3)
Based on the above two equations the wind power is
3
2
1AvP ρ= (246)
The specific power or power density of a wind site is given as
3
2
1v
A
PPden ρ== (247)
It is noted that the specific power of a wind site is proportional to the cube of the
wind speed
Power Extracted from Wind The actual power extracted by the rotor blades from
wind is the difference between the upstream and the down stream wind powers
)(2
1 2
0
2 vvkP m minus= (248)
50
where v is the upstream wind velocity at the entrance of the rotor blades v0 is the
downstream wind velocity at the exit of the rotor blades km is the mass flow rate which
can be expressed as
2
0vvAkm
+= ρ (249)
where A is the area swept by the rotor blades
From (248) and (249) the mechanical power extracted by the rotor is given by
)(22
1 2
0
20 vvvv
AP minus
+= ρ (250)
Let
minusminus
+=
2
00 1112
1
v
v
v
vC p and rearrange the terms in (250) we have
pCAvP 3
2
1ρ= (251)
Cp is called the power coefficient of the rotor or the rotor efficiency It is the fraction
of the upstream wind power which is captured by the rotor blades and has a theoretical
maximum value of 059 shown in Figure 23 In practical designs maximum achievable
Cp is between 04 and 05 for high-speed two-blade turbines and between 02 and 04 for
low-speed turbines with more blades [211]
It is noted from (251) that the output power of a turbine is determined by the
effective area of the rotor blades (A) wind speed (v) and wind flow conditions at the
rotor (Cp) Thus the output power of the turbine can be varied by changing the effective
area andor by changing the flow conditions at the rotor system Control of these
quantities forms the basis of control of wind energy systems
51
0 02 04 06 08 10
01
02
03
04
05
06
07
v0 v
Cp
Figure 23 Theoretical rotor efficiency vs v0v ratio
Tip Speed Ratio The tip speed ratio λ (TSR) defined as the ratio of the linear speed
at the tip of the blade to the free stream wind speed is given as follows [211]
v
Rωλ = (252)
where R is the rotor blade radius and ω is the rotor angular speed
TSR is related to the wind turbine operating point for extracting maximum power
The maximum rotor efficiency Cp is achieved at a particular TSR which is specific to the
aerodynamic design of a given wind turbine For variable TSR turbines the rotor speed
will change as wind speed changes to keep TSR at some optimum level Variable TSR
turbines can produce more power than fixed TSR turbines [212]
52
Wind Energy Conversion System The block diagram of a typical wind energy
conversion system is shown in Figure 24
Figure 24 Block diagram of a typical wind energy conversion system
The principle components of a modern wind turbine are the tower the yaw the rotor
and the nacelle which accommodates the gear box and the generator The tower holds the
53
main part of the wind turbine and keeps the rotating blades at a height to capture
sufficient wind power The yaw mechanism is used to turn the wind turbine rotor blades
against the wind Wind turbine captures the windrsquos kinetic energy in the rotor consisting
of two or more blades The gearbox transforms the slower rotational speeds of the wind
turbine to higher rotational speeds on the electrical generator side Electrical generator
will generate electricity when its shaft is driven by the wind turbine whose output is
maintained as per specifications by employing suitable control and supervising
techniques In addition to monitoring the output these control systems also include
protection equipment to protect the overall system [211]
Two distinctly different design configurations are available for a wind turbine the
horizontal axis configuration and the vertical axis configuration The vertical axis
machine has the shape like an egg beater (also called the Darrieus rotor after its inventor)
However most modern turbines use horizontal axis design [211]
Constant Speed and Variable Speed Wind Energy Conversion Systems (WECS)
Generally there are two types of wind energy conversion systems constant speed and
variable speed systems shown in Figure 25 [212] In Figure 25 (a) the generator
normally is a squirrel cage induction generator which is connected to a utility grid or load
directly Since the generator is directly coupled the wind turbine rotates at a constant
speed governed by the frequency of the utility grid (50 or 60 Hz) and the number of poles
of the generator The other two wind power generation systems shown in Figure 25 (b)
and (c) are variable speed systems In Figure 25 (b) the generator is a doubly-fed
induction generator (wound rotor) The rotor of the generator is fed by a back-to-back
54
converter voltage source converter The stator of the generator is directly connected to
load or grid Through proper control on the converter for the rotor the mechanical speed
of the rotor can be variable while the frequency of output AC from the stator can be kept
constant Figure 25 (c) shows a variable speed system which is completely decoupled
from load or grid through a power electronic interfacing circuit The generator can either
be a synchronous generator (with excitation winding or permanent magnet) or an
induction generator In this dissertation a variable speed WECS similar to the one shown
in Figure 25 (c) is used for the hybrid energy system study The generator used in the
study is a self-excited induction generator
Wind Turbine Output Power vs Wind Speed A typical power vs wind speed curve
is shown in Figure 26 [212] [215] When the wind speed is less than the cut-in speed
(normally 3-5 ms) [212] there is no power output Between the cut-in speed and the
rated or nominal wind speed (normally 11-16 ms) [212] the wind turbine output power
is directly related to the cubic of wind speed as given in (251) When the wind speed is
over the nominal value the output power needs to be limited to a certain value so that the
generator and the corresponding power electronic devices (if any) will not be damaged
In other words when the wind speed is greater than the rated value the power coefficient
Cp needs to be reduced [see (251)] When the wind speed is higher than the cut-out speed
(normally 17-30 ms) [212] the system will be taken out of operation for protection of
its components
55
Figure 25 Constant and variable speed wind energy conversion systems [212]
56
Figure 26 Typical curves for a constant speed stall controlled (dotted) and variable speed pitch controlled (solid) wind turbine [212] [215]
There are several ways to control the wind turbine output power The two common
ways to achieve this goal are stall control and pitch control [211]-[215]
For a stall controlled wind turbine there is no active control applied to it The output
power is regulated through a specifically designed rotor blades The design ensures that
when the wind speed is too high it creates turbulences on the side of the rotor blades The
turbulences will decrease the aerodynamic efficiency of the wind turbine as a result
Pitch control is an active method which is used to reduce the aerodynamic efficiency
by changing pitch angle (turning the rotor blades out of wind) of the rotor blades It
should be noted that the pitch angle can change at a finite rate which may be quite low
due to the size of the rotor blades The maximum rate of change of the pitch angle is in
the order of 3 to 10 degreessecond [215]
It is noted from Figure 26 that a variable speed system normally has lower cut-in
speed The rated speed is also normally lower than a constant speed system For wind
57
speeds between the cut-in and the nominal speed there will be 20-30 increase in the
energy capture with variable speed compared to the fixed-speed operation[211]-[215]
shown in Figure 26 For a pitch controlled wind system the power for wind speeds over
the nominal value can be held constant precisely On the other hand for a stall controlled
constant speed system the output power will reach its peak value somewhat higher than
its rated value and then decreases as wind speed grows
Photovoltaic Energy System
Terminology
Solar radiation Also called insolation consists of the radiation that comes directly
from the sun (beam radiation) as well as the radiation that comes indirectly (diffusion and
albedo radiation) [216]
Solar constant The solar radiation that falls on a unit area above the atmosphere at a
vertical angle is called solar constant It has a value of 1367 Wmsup2 [216]
Air mass A convenient lumped parameter used for the amount of sunlight absorbed in
the atmosphere The amount of beam solar radiation absorbed in the atmosphere in a
direct vertical path to sea level is designated as one air mass (AM1) In general air mass
is proportional to the secant of the zenith angle [216]
Irradiance A measure of power density of sunlight it has a unit of Wm2
Irradiation A measure of energy density (Jm2) it is the integral of irradiance over
time
Photovoltaic effect is a basic physical process through which solar energy is
converted into electrical energy directly The physics of a PV cell or solar cell is similar
58
to the classical p-n junction diode shown in Figure 27 [211] At night a PV cell can
basically be considered as a diode When the cell is illuminated the energy of photons is
transferred to the semiconductor material resulting in the creation of electron-hole pairs
The electric field created by the p-n junction causes the photon-generated electron-hole
pairs to separate The electrons are accelerated to n-region (N-type material) and the
holes are dragged into p-region (P-type material) shown in Figure 27 The electrons
from n-region flow through the external circuit and provide the electrical power to the
load at the same time
Figure 27 Schematic block diagram of a PV cell
The PV cell shown in Figure 27 is the basic component of a PV energy system Since
a typical PV cell produces less than 2 W at approximately 05 V DC it is necessary to
connect PV cells in series-parallel configurations to produce desired power and voltage
ratings Figure 28 shows how single PV cells are grouped to form modules and how
modules are connected to build arrays There is no fixed definition on the size of a
module and neither for an array A module may have a power output from a few watts to
59
hundreds of watts And the power rating of an array can vary from hundreds of watts to
megawatts [211] [216]
Figure 28 PV Cell module and array
Fuel Cells
Fuel cells (FCs) are static energy conversion devices that convert the chemical energy
of fuel directly into DC electrical energy [217]-[218] The basic physical structure of a
fuel cell consists of two porous electrodes (anode and cathode) and an electrolyte layer in
the middle Figure 29 shows a schematic diagram of a polymer electrolyte membrane
fuel cell (PEMFC) The electrolyte layer is a good conductor for ions (positive or
negative charged) but not for electrons The electrolyte can either be solid such as
PEMFC and solid oxide fuel cells (SOFC) or liquid such as molten carbonate fuel cells
(MCFC) The type and chemical properties of the electrolyte used in fuel cells are very
60
important to their operating characteristics such as their operating temperatures
The polarity of an ion and its transport direction can differ for different fuel cells
determining the site of water production and removal If the working ion is positive like
in a PEMFC shown in Figure 29 then water is produced at the cathode On the other
hand if the working ion is negative like SOFC and MCFC shown in Figures 211 and
213 water is formed at the anode In both cases electrons have to pass through an
external circuit and produce electric current
In a typical fuel cell fuel is fed continuously to the anode and oxidant is fed
continuously to the cathode The electrochemical reactions take place at the electrodes to
convert chemical energy into electricity Note that anode is the electrode from which
electrons leave (negative) and cathode is the electrode to which the electrons are coming
(positive) The most common used fuel for fuel cells is hydrogen and the oxidant is
usually oxygen or air Nevertheless theoretically any substance capable of chemical
oxidation that can be supplied continuously (as a fluid) can be used as fuel at the anode of
a fuel cell Similarly the oxidant can be any fluid that can be reduced at a sufficient rate
[219]
Among different types of fuel cells SOFC PEMFC and MCFC are most likely to be
used for distributed generation (DG) applications [217]-[218] [220]-[224] Compared
with conventional power plants these FCDG systems have many advantages such as high
efficiency zero or low emission (of pollutant gases) and flexible modular structure In the
following an overview is given on the operating principles of the above three types of
fuel cells Though MCFC is out of the scope of this dissertation it is also included here
as a potential candidate for fuel cell DG applications
61
PEMFC PEMFC has a sandwich like structure as shown in Figure 29 [217]
[218] [220] Between two porous electrodes is a Teflon-like membrane which is an
excellent conductor of protons and an insulator of electrons [217] [218] The hydrogen
molecules are broken into electrons and hydrogen protons at the anode with the help of
platinum catalyst The hydrogen protons pass through the membrane (electrolyte) reach
the cathode surface and combine with the electrons which travel from anode to cathode
through the external load to produce water The reactions at the anode and cathode side
and the overall reaction are given in Figure 29
Gas
Flow
Channel Anode
Electron
Flow
Cathode
Membrane
Catalyst
Layers
H2
H2O
O24H+
Load
4e- 4e-
Gas
Flow
Channel
2H2+ O
2 = 2H
2O
Current
Flow
Figure 29 Schematic diagram of a PEMFC
One of the advantages of the PEMFC is its high power density and high efficiency
(40-45) This makes the technology competitive in transportation and stationary
applications Another benefit is its lower operating temperature (between 60degC and 80degC)
62
and because of this the PEMFC has a quick start which is beneficial in automotive
applications where quick start is necessary
5 10 15 20 2522
24
26
28
30
32
34
36
38
40
Load Current (A)
PEMFC Output Voltage (V)
ActivationRegion
Ohmic Region
Concentration Region
Figure 210 V-I characteristic of a 500W PEMFC stack [220]
Figure 210 shows the output voltage vs load current (V-I) characteristic curve of a
500W PEMFC stack [220] This characteristic curve which is typical of other fuel cells
can be divided into three regions The voltage drop across the fuel cell associated with
low currents is due to the activation loss inside the fuel cell the voltage drop in the
middle of the curve (which is approximately linear) is due to the ohmic loss in the fuel
cell stack and as a result of the concentration loss the output voltage at the end of the
curve will drop sharply as the load current increases [217] [218]
63
SOFC SOFC is a high temperature fuel cell technology with a promising future
Based on a negative-ion conductive electrolyte SOFCs operate between 600 C and 1000
C and convert chemical energy into electricity at high efficiency which can reach up to
65 [221] The overall efficiency of an integrated SOFC-combustion turbine system can
even reach 70 [221] Despite slow start-up and more thermal stresses due to the high
operating temperature SOFC allows for internal reforming of gaseous fuel inside the fuel
cell which gives multi-fuel capability to SOFCs [217] [218] Moreover their solid
nature simplifies system designs where the corrosion and management problems related
to liquid electrolyte are eliminated [217] These merits give SOFC a bright future to be
used in stationary applications Figure 211 shows a block diagram of a SOFC The
reactions at the anode and cathode are also given in the figure
Figure 211 Schematic diagram of a SOFC
64
The steady-state terminal V-I curves of a 5kW SOFC model (which will be discussed
in detail in Chapter 4) at different temperatures which are typical of SOFCs are shown
in Figure 212 [223] The activation voltage drop dominates the voltage drop in the
low-current region As load current increases the ohmic voltage drop increases fast and
becomes the main contribution to the SOFC voltage drop When load current exceeds a
certain value fuel cell output voltage will drop sharply due to the concentration voltage
drop inside SOFC Figure 212 also shows the effect of temperature on SOFC V-I
characteristic curve SOFC output voltage is higher at lower temperature in the low
current zone while the voltage is higher at higher temperature in the high current region
0 50 100 1500
20
40
60
80
100
120
Load current (A)
SOFC output voltage (V)
1073K
1173K
1273K
Figure 212 V-I characteristic of a 5kW SOFC stack [223]
65
MCFC MCFCs use a molten mixture of alkali metal carbonate as their electrolyte
[217] [218] At high temperatures (600oC ndash 700 oC) the salt mixture is in liquid phase
and is an excellent conductor of minus23CO ions At the cathode the oxygen and carbon oxide
combine with the electrons flowing through the external circuit to produce carbonate ions
( minus23CO ) At the anode minus2
3CO ions are deoxidized by hydrogen and electrons are released
at the same time These electrons will have to go through the external circuit and then
reach the cathode surface Figure 213 shows the schematic diagram of a MCFC The
reactions at the anode and cathode side are given in the figure -
2 3
-
22
2CO
4e
2CO
O
=+
+
-
2
-2 3
24e
2CO
2CO
2H+
=+
Figure 213 Schematic diagram of a MCFC
Figure 214 shows the V-I performance progress for MCFCs from 1967 to 2002
[217] During the 1980s the performance of MCFC stacks made dramatic
improvements It is noted from this figure that MCFCs normally operate in the range of
100-200 mAcm2 at 750-850 mV for a single cell [217] MCFs have achieved
66
efficiencies in the range of 50-60 before heat recovery and with heat recovery their
efficiency could exceed 70 [224]
Figure 214 Progress in generic performance of MCFCs on reformate gas and air
Electrolyzer
An electrolyzer is a device that produces hydrogen and oxygen from water Water
electrolysis can be considered a reverse process of a hydrogen fueled fuel cell Opposite
to the electrochemical reaction occurring in fuel cell an electrolyzer converts the DC
electrical energy into chemical energy stored in hydrogen
Water electrolysis is a long-established process which started in the early part of
nineteen century [225] Nicholson and Carlisle English chemists first discovered the
phenomenon of electrolytic decomposition in acid water in 1800 However alkaline
medium is preferred in todayrsquos industrial electrolysis plants Currently there are three
principal types of electrolyzer available in the market alkaline PEM and solid oxide
67
The alkaline and PEM electrolyzers are well established devices with thousands of units
in operation while the solid-oxide electrolyzer is as yet unproven [226] Alkaline water
electrolysis is the dominating technology today In this section the principle of alkaline
water electrolysis is reviewed
An alkaline electrolyzer uses potassium hydroxide (KOH) as electrolyte solution for
transferring hydroxyl ions Figure 215 shows the schematic diagram of an alkaline
electrolyzer At the cathode two water molecules are reduced electrochemically (by the
two electrons from the cathode) to one molecule of H2 and two hydroxyl ions (OH-) The
reaction at the cathode can be expressed as
minusminus +uarrrarr+ OHHeOH 222 22 (253)
Under the external electric field the hydroxyl ions are forced to move towards the
anode through the porous diaphragm At the anode the two molecule hydroxyl ions
losing two electrons to the anode are discharged into 12 molecule of O2 and one
molecule of water The chemical reaction at the cathode is
minusminus ++uarrrarr eOHOOH 22
12 22 (254)
By combining the above two equations the overall chemical reaction inside an
electrolyzer is
uarr+uarrrarr 2222
1OHOH (255)
68
Figure 215 Schematic diagram of an alkaline electrolyzer
The current density of alkaline electrolyzers is normally less than 04 Acm2 The
energy conversion efficiencies can range from 60-90 Without auxiliary purification
equipment purities of 998 for H2 can be achieved Alkaline electrolysis technology
can be implemented at a variety of scales from less than 1 kW to large industrial
electrolyzer plant over 100 MW as long as there is a proper DC electricity supply [227]
69
Summary
In this chapter the fundamental concepts and principles of energy systems and energy
conversion are reviewed The chapter begins with the introduction of the basic energy
forms and then reviews the fundamentals of thermodynamics and electrochemistry The
First and Second Law of Thermodynamics the maximum conversion efficiency of a
conventional heat engine heat transfer the concepts of enthalpy entropy and the Gibbs
energy and the well-known Nernst equation are briefly explained The fundamentals of
wind energy conversion systems photovoltaic systems fuel cells and electrolyzers are
also reviewed The principles reviewed in this chapter are the fundamentals needed for
modeling the proposed multi-source alternative energy system discussed in the following
chapters
70
REFERENCES
[21] Archie W Culp Jr Principles of Energy Conversion McGraw-Hill Book Company 1979
[22] Steven S Zumdahl Chemical Principles 2nd Edition DC Heath and Company Toronto 1995
[23] FT Ulaby Fundamentals of Applied Electromagnetics Prentice-Hall Inc 1999
[24] ERG Eckert and R M Drake Jr Analysis of Heat and Mass Transfer McGraw-Hill Book Company 1972
[25] George N Hatsopoulos and Joseph H Keenan Principles of General
Thermodynamics John Wiley amp Sons Inc 1965
[26] E L Harder Fundamentals of Energy Production John Wiley amp Sons 1982
[27] FA Farret and MG Simotildees Integration of Alternative Sources of Energy John Wiley amp Sons Inc 2006
[28] G Hoogers Fuel Cell Technology Handbook CRC Press LLC 2003
[29] JANAF Thermochemical Tables 2nd Edition NSRDS-NBS 37 1971
[210] G Kortum Treatise on Electrochemistry (2nd Edition) Elsevier Publishing Company 1965
[211] M R Patel Wind and Solar Power Systems CRC Press LLC 1999
[212] JG Slootweg ldquoWind power modeling and impact on power system dynamicsrdquo PhD dissertation Dept Elect Eng Delft University of Technology Delft Netherlands 2003
[213] JF Manwell JG McGowan and AL Rogers Wind energy Explained ndash Theory
Design and Application John Wileyamp Sons 2002
[214] Tony Burton David sharpe Nick Jenkins and Ervin Bossanyi Wind Energy
Handbook John Wileyamp Sons 2001
[215] SR Guda ldquoModeling and power management of a hybrid wind-microturbine power generation systemrdquo MS thesis Montana State University 2005
71
[216] R Messenger and J Ventre Photovoltaic Systems Engineering CRC Press LLC 2000
[217] Fuel Cell Handbook (Sixth Edition) EGampG Services Inc Science Applications International Corporation DOE Office of Fossil Energy National Energy Technology Lab Nov 2002
[218] James Larminie and Andrew Dicks Fuel Cell Systems Explained 2nd Edition John Wiley amp Sons Ltd 2003
[219] AJ Appleby FR Foulkes Fuel Cell Handbook Van Nostrand Reinhold New York NY 1989
[220] C Wang MH Nehrir and SR Shaw ldquoDynamic Models and Model Validation for PEM Fuel Cells Using Electrical Circuitsrdquo IEEE Transactions on Energy Conversion Vol 20 No 2 pp442-451 June 2005
[221] O Yamamoto ldquoSolid oxide fuel cells fundamental aspects and prospectsrdquo Electrochimica Acta Vol 45 No (15-16) pp 2423-2435 2000
[222] J Padulleacutes GW Ault and J R McDonald ldquoAn integrated SOFC plant dynamic model for power system simulationrdquo J Power Sources pp495ndash500 2000
[223] C Wang and MH Nehrir ldquoA Dynamic SOFC Model for Distributed Power Generation Applicationsrdquo Proceedings 2005 Fuel Cell Seminar Palm Springs CA Nov 14-18 2005
[224] MD Lukas KY Lee H Ghezel-Ayagh ldquoAn Explicit Dynamic Model for Direct Reforming Carbonate Fuel Cell Stackrdquo IEEE Transactions on Energy Conversion Vol 16 No 3 pp 289-295 Sept 2000
[225] W Kreuter and H Hofmann ldquoElectrolysis The Important Energy Transformer in a World of Sustainable Energyrdquo Int J Hydrogen Energy Vol 23 No8 pp 661-666 1998
[226] M Newborough ldquoA Report on Electrolysers Future Markets and the Prospects for ITM Power Ltdrsquos Electrolyser Technologyrdquo Online http wwwh2fccomNewsletter
[227] AFG Smith and M Newborough ldquoLow-Cost Polymer Electrolysers and Electrolyser Implementation Scenarios for Carbon Abatementrdquo Report to the Carbon Trust and ITM-Power PLC Nov 2004
72
CHAPTER 3
MULTI-SOURCE ALTERNATIVE ENERGY
DISTRIBUTED GENERATION SYSTEM
Introduction
The ever increasing energy consumption the soaring cost and the exhaustible nature
of fossil fuel and the worsening global environment have created booming interest in
green (renewable energy source or fuel cell based) power generation systems Compared
to the conventional centralized power plants these systems are sustainable smaller in
size and (some) can be installed closer to load centers The power is delivered to
customers by many distributed generation (DG) systems other than the conventional way
that power is transmitted from centralized power plants to load centers over transmission
lines and then through distribution systems Due to steady progress in power deregulation
and utility restructuring and tight constraints imposed on the construction of new
transmission lines for long distance power transmission DG applications are expected to
increase in the future
Wind and solar power generation are two of the most promising renewable power
generation technologies The growth of wind and photovoltaic (PV) power generation
systems has exceeded the most optimistic estimation Fuel cells also show great potential
to be green power sources of the future because of many merits they have (such as high
efficiency zero or low emission of pollutant gases and flexible modular structure) and
73
the rapid progress in fuel cell technologies However none of these technologies is
perfect now Wind and solar power are highly dependent on climate while fuel cells need
hydrogen-rich fuel and the cost for fuel cells is still very high at current stage
Nevertheless because different renewable energy sources can complement each other
multi-source hybrid alternative energy systems (with proper control) have great potential
to provide higher quality and more reliable power to customers than a system based on a
single resource And because of this hybrid energy systems have caught worldwide
research attention [31]-[334]
There are many combinations of different alternative energy sources and storage
devices to build a hybrid system The following lists some of the stand-alone or
grid-connected hybrid systems that have been reported in the literature
1) WindPVFCelectrolyzerbattery system [31]-[33]
2) Micro-turbineFC system [34]-[35]
3) Microturbinewind system [36]
4) Gas-turbineFC system [37]-[39]
5) DieselFC system [310]-[311]
6) PVbattery [312]
7) PVFCelectrolyzer [313]-[315]
8) PVFCelectrolyzerbattery system [316]-[318]
9) FCbattery or super-capacitor system [319]-[320]
10) WindFC system [321]
11) Winddiesel system [322]
12) WindPVbattery system [323]-[325]
74
13) PVdiesel system [326]
14) DieselwindPV system [327]
15) PVFC Super-conducting Magnetic Energy Storage (SMES) system [328]
From the above listed hybrid energy systems it is noted that the main renewable
energy sources are wind and photovoltaic power Due to natural intermittent properties of
wind and photovoltaic power stand-alone wind andor PV renewable energy systems
normally require energy storage devices or some other generation sources to form a
hybrid system The storage device can be a battery bank super-capacitor bank SMES or
a FC-electrolyzer system
In this study a multi-source hybrid alternative distributed generation system
consisting of wind PV fuel cell electrolyzer and battery is proposed Wind and
photovoltaic are the primary power sources of the system to take full advantage of
renewable energy around us The FCelectrolyzer combination is used as a backup and
long term storage system For a stand-alone application a battery is also used in the
system as short term energy storage to supply fast transient and ripple power In the
proposed system the different energy sources are integrated through an AC link bus
(discussed later in this chapter) An overall power management controller is designed for
the system to coordinate the power flows among the different energy sources The details
of the system configuration are discussed in this chapter The system component
modeling will be discussed in Chapter 4 The system control scheme and simulation
results under different scenarios will be given in Chapter 7
75
Figure 31 Hybrid energy system integration DC coupling
AC Coupling vs DC Coupling
There are several ways to integrate different alternative energy sources to form a
hybrid system The methods can be generally classified into two categories DC coupling
and AC coupling AC coupling can be classified further into power frequency AC (PFAC)
coupling and high frequency AC (HFAC) coupling In a DC coupling configuration
shown in Figure 31 different alternative energy sources are connected to a DC bus
through appropriate power electronic interfacing circuits Then the DC energy is
converted into 60 Hz (or 50 Hz) AC through a DCAC converter (inverter) which can be
bi-directional
76
(a)
(b) Figure 32 Hybrid energy system integration (a) PFAC coupling (b) HFAC coupling
77
In a PFAC coupling scheme shown in Figure 32 (a) different energy sources are
integrated through proper power electronic interfacing circuits to a power frequency AC
bus Coupling inductors may also be needed to achieve desired power flow management
In a HFAC link scheme shown in Figure 32 (b) different alternative energy sources are
coupled to a HFAC bus HFAC loads are connected directly to the HFAC bus The HFAC
can also be converted into PFAC through an ACAC converter so that regular AC loads
can be connected to the PFAC bus HFAC link is originally developed for supplying
power to HFAC loads This configuration has been used mostly in applications with
HFAC (eg 400 Hz) loads such as airplanes vessels submarines and space station
applications [329]
Different coupling schemes find their own appropriate applications DC coupling is
the simplest and the oldest type of integration PFAC link is more modular than DC
scheme and is ready for grid connection HFAC coupling is more complicated and is
more suitable for the applications with HFAC loads Table 31 summaries the advantages
and disadvantages of each coupling scheme
78
TABLE 31 COMPARISON AMONG DIFFERENT INTEGRATION SCHEMES
Coupling Scheme
Advantage Disadvantage
DC [31]-[32] [312]
[329]-[330]
1 Synchronism not needed 2 Suitable for long distance
transmission it has less transmission losses
3 Single-wired connection
1 Concerns on the voltage compatibility
2 Corrosion concerns with the DC electrodes
3 Non-standard connection requires high costs in installing and maintenance
4 If the DCAC inverter is out of service the whole system fails to supply AC power
PFAC [329]
[331]-[332]
1 High reliability If one of the energy sources is out of service it can be isolated from the system easily
2 Ready for grid connection 3 Standard interfacing and
modular structure 3 Easy multi-voltage and
multi-terminal matching 4 Well established scale economy
1 Synchronism required 2 The need for power factor and harmonic distortion correction
3 Not suitable for long distance transmission
HFAC [329]
[333]-[334]
1 Higher order harmonics can be easily filtered out
2 Suitable for applications with HFAC loads with improved efficiency
3 Size of high frequency transformers harmonic filters and other passive components are smaller
1 Complex control 2 Higher component and maintenance costs due to high frequency
3 The dependence on future advances of power electronics
4 Concerns about electromagnetic compatibility
5 Extremely limited capability of long distance transmission
79
Stand-alone vs Grid-connected Systems
A hybrid alternative energy system can either be stand-alone or grid-connected if
utility grid is available For a stand-alone application the system needs to have sufficient
storage capacity to handle the power variations from the alternative energy sources
involved A system of this type can be considered as a micro-grid which has its own
generation sources and loads [335] For a grid-connected application the alternative
energy sources in the micro-grid can supply power both to the local loads and the utility
grid In addition to real power these DG sources can also be used to give reactive power
and voltage support to the utility grid The capacity of the storage device for these
systems can be smaller if they are grid-connected since the grid can be used as system
backup However when connected to a utility grid important operation and performance
requirements such as voltage frequency and harmonic regulations are imposed on the
system [336] Both grid-connected and stand-alone applications will be discussed in the
later chapters The optimal placement of DG sources in power systems will also be
discussed in Chapter 8
The Proposed System Configuration
Figure 33 shows the system configuration for the proposed hybrid alternative energy
system In the system the renewable wind and solar power are taken as the primary
source while fuel cellelectrolyzer combination is used as a backup and storage system
This system can be considered as a complete ldquogreenrdquo power generation system because
the main energy sources and storage system are all environmentally friendly and it can be
80
stand-alone or grid-connected When there is excess wind andor solar generation
available the electrolyzer turns on to begin producing hydrogen which is delivered to the
hydrogen storage tanks If the H2 storage tanks become full the excess power will be
diverted to other dump loads which are not shown in Figure 33 When there is a deficit
in power generation the fuel cell stack will begin to produce energy using hydrogen from
the reservoir tanks or in case they are empty from the backup H2 tanks A battery bank is
used to supply transient power to fast load transients ripples and spikes in stand-alone
applications For grid-connected applications the battery bank can be taken out from the
system the utility grid will take care of transient power Different energy sources are
connected to a 60 Hz AC bus through appropriate power electronic interfacing circuits
The system can be easily expended ie other energy sources can be integrated into the
system when they are available as shown in Figure 33 The main system components
and their sizes are discussed in the following section
System Unit Sizing
The unit sizing procedure discussed in this section is assumed for a stand-alone
hybrid system with the proposed structure (Figure 33) for residential electricity supply in
southwestern part of Montana The hybrid system is designed to supply power for five
homes A typical load demand for each home reported in [337] in the Pacific Northwest
regions is used in this simulation study The total load demand of the five homes is shown
in Figure 34 A 50 kW wind turbine is assumed to be available already for the hybrid
system The following unit sizing procedure is used to determine the size of PV arrays
fuel cells the electrolyzer and the battery
81
Figure 33 System configuration of the proposed multi-source alternative hybrid energy system (coupling inductors are not shown in the figure)
82
0 4 8 12 16 20 240
5
10
15
Time (Hour of Day)
Demand (kW)
Figure 34 Hourly average demand of a typical residence in the Pacific Northwest area
Before the discussion of unit sizing the following concept is applied for indicating
the overall efficiency and availability of a renewable energy source
Capacity factor of a renewable energy kcf is defined as
Actual average output power over a period of time T kcf =
Nominal power rating of the renewable energy source (31)
For the wind and solar data reported in [33] [324] the capacity factor of the wind
turbine (kcf_wtg) and the PV (kcf_pv) array used in the proposed hybrid system for the
southwestern part of Montana are taken as 13 and 10 respectively
The purpose of unit sizing is to minimize the difference between the generated power
( genP ) from the renewable energy source and the demand (demP ) over a period of time T T
is taken as one year in this study
83
demratedpvpveffratedwtgwtgeffdemgen PPkPkPPP minustimes+times=minus=∆ __ (32)
where Pwtgrated is the power rating of the wind turbine generator and Pwtgpv is the power
rating the PV array
To balance the generation and the demand the rated power for the PV arrays is
( )pveffratedwtgwtgeffdemratedpv kPkPP __ timesminus= (33)
From Figure 34 the average load demand is 976 kW Then according to (33) the
size of the PV array is calculated to be 326 kW
The FCelectrolyzer combination is taken as the storage for the system The fuel cell
needs to supply the peak load demand when there is no wind and solar power Therefore
the size of fuel cell is 146 kW (Figure 34) To leave some safe margin an 18 kW fuel
cell stack array is used
The electrolyzer should be able to handle the excess power from the wind and solar
power source The maximum possible excess power is
(Pgen - Pdem)max = 766 kW (34)
However the possibility that both the wind and solar power reach their maximum
points while the load demand is at its lowest value is very small According to the data
reported in [330] the excess available power normally is less than half of the maximum
possible value And electrolyzer is also very expensive Therefore a 50 kW electrolyzer
[over 60 of the maximum available given in (34)] is used in this study
Battery capacity can be determined based on the transient power at the load site In
this study a 10 kWh battery bank is used
The details of the system component parameters are listed in Table 32
84
TABLE 32 COMPONENT PARAMETERS OF THE PROPOSED HYBRID ENERGY SYSTEM
Wind turbine
Rated power 50 kW
Cut in speed (Cut out speed) 3 ms (25 ms)
Rated speed 14 ms
Blade diameter 15 m
Gear box ratio 75
Induction generator
Rated power 50 kW
Rated voltage 670 V
Rated frequency 60 Hz
PV array
Module unit 153 cells 173 W 1 kWm2 25 ˚C
Module number 16times12 = 192
Power rating 192times173 asymp 33 kW
Fuel cell array
PEMFC stack 500 W
PEMFC array 6times6 = 36
PEMFC array power rating 36times05 = 18 kW
Or SOFC stack 5 kW
SOFC array 2times2 = 4
SOFC array power rating 4times5 kW = 20 kW
Electrolyzer
Rated power 50 kW
Number of cells 40 (in series)
Operating voltage 60 - 80 V
Battery
Capacity 10 kWh
Rated voltage 400 V
85
REFERENCES
[31] K Agbossou M Kolhe J Hamelin and TK Bose ldquoPerformance of a stand-alone renewable energy system based on energy storage as hydrogenrdquo IEEE
Transactions on Energy Conversion Vol 19 No 3 pp 633 ndash 640 Sept 2004
[32] K Agbossou R Chahine J Hamelin FLaurencelle A Anourar J-M St-Arnaud and TK Bose ldquoRenewable energy systems based on hydrogen for remote applicationsrdquo Journal of Power Sources Vol 96 pp168-172 2001
[33] DB Nelson MH Nehrir and C Wang ldquoUnit Sizing and Cost Analysis of Stand-Alone Hybrid WinPVFuel Cell Systemsrdquo Renewable Energy (accepted)
[34] R Lasseter ldquoDynamic models for micro-turbines and fuel cellsrdquo Proceedings 2001 PES Summer Meeting Vol 2 pp 761-766 2001
[35] Y Zhu and K Tomsovic ldquoDevelopment of models for analyzing the load-following performance of microturbines and fuel cellsrdquo Journal of Electric Power Systems Research pp 1-11 Vol 62 2002
[36] SR Guda C Wang and MH Nehrir ldquoModeling of Microturbine Power Generation Systemsrdquo Journal of Power Components amp Systems (accepted)
[37] K Sedghisigarchi and A Feliachi ldquoDynamic and Transient Analysis of Power Distribution Systems with Fuel CellsmdashPart I Fuel-Cell Dynamic Modelrdquo IEEE Transactions on Energy Conversion Vol 19 No 2 pp423-428 June 2004
[38] K Sedghisigarchi and A Feliachi ldquoDynamic and Transient Analysis of Power Distribution Systems with Fuel CellsmdashPart II Control and Stability Enhancementrdquo IEEE Transactions on Energy Conversion Vol 19 No 2 pp429-434 June 2004
[39] SH Chan HK Ho and Y Tian ldquoMulti-level modeling of SOFC-gas turbine hybrid systemrdquo International Journal of Hydrogen Energy Vol 28 No 8 pp 889-900 Aug 2003
[310] Z Miao M A Choudhry R L Klein and L Fan ldquoStudy of A Fuel Cell Power Plant in Power Distribution System ndash Part I Dynamic Modelrdquo Proceedings IEEE PES General Meeting June 2004 Denver CO
[311] Z Miao M A Choudhry R L Klein and L Fan ldquoStudy of A Fuel Cell Power Plant in Power Distribution System ndash Part II Stability Controlrdquo Proceedings IEEE PES General Meeting June 2004 Denver CO
86
[312] H Dehbonei ldquoPower conditioning for distributed renewable energy generationrdquo PhD Dissertation Curtin University of Technology Perth Western Australia 2003
[313] P A Lehman CE Chamberlin G Pauletto MA Rocheleau ldquoOperating Experience with a photovoltaic-hydrogen energy systemrdquo Proceedings
Hydrogenrsquo94 The 10th World Hydrogen Energy Conference Cocoa Beach FL June 1994
[314] A Arkin and J J Duffy ldquoModeling of PV Electrolyzer and Gas Storage in a Stand-Alone Solar-Fuel Cell Systemrdquo Proceedings the 2001 National Solar Energy Conference Annual Meeting American Solar Energy Society 2001
[315] L A Torres F J Rodriguez and PJ Sebastian ldquoSimulation of a solar-hydrogen-fuel cell system results for different locations in Mexicordquo International Journal of Hydrogen Energy Vol 23 No 11 pp 1005-1010 Nov 1998
[316] S R Vosen and JO Keller ldquoHybrid energy storage systems for stand-alone electric power systems optimization of system performance and cost through control strategiesrdquo International Journal of Hydrogen Energy Vol 24 No 12 pp 1139-56 Dec 1999
[317] Th F El-Shatter M N Eskandar and MT El-Hagry ldquoHybrid PVfuel cell system design and simulationrdquo Renewable Energy Vol 27 No 3 pp479-485 Nov 2002
[318] Oslash Ulleberg and S O MOslashRNER ldquoTRNSYS simulation models for solar-hydrogen systems rdquo Solar Energy Vol 59 No 4-6 pp 271-279 1997
[319] J C Amphlett EH de Oliveira RF Mann PR Roberge and Aida Rodrigues ldquoDynamic Interaction of a Proton Exchange Membrane Fuel Cell and a Lead-acid Batteryrdquo Journal of Power Sources Vol 65 pp 173-178 1997
[320] D Candusso L Valero and A Walter ldquoModelling control and simulation of a fuel cell based power supply system with energy managementrdquo Proceedings 28th Annual Conference of the IEEE Industrial Electronics Society (IECON 2002) Vol 2 pp1294-1299 2002
[321] M T Iqbal ldquoModeling and control of a wind fuel cell hybrid energy systemrdquo Renewable Energy Vol 28 No 2 pp 223-237 Feb 2003
[322] H Sharma S Islam and T Pryor ldquoDynamic modeling and simulation of a hybrid wind diesel remote area power systemrdquo International Journal of Renewable Energy Engineering Vol 2 No1 April 2000
87
[323] R Chedid H Akiki and S Rahman ldquoA decision support technique for the design of hybrid solar-wind power systemsrdquo IEEE Transactions on Energy Conversion Vol 13 No 1 pp 76-83 March 1998
[324] W D Kellogg M H Nehrir G Venkataramanan and V Gerez ldquoGeneration unit sizing and cost analysis for stand-alone wind photovoltaic and hybrid windPV systemsrdquo IEEE Transactions on Energy Conversion Vol 13 No 1 pp 70-75 March 1998
[325] F Giraud and Z M Salameh ldquoSteady-state performance of a grid-connected rooftop hybrid wind-photovoltaic power system with battery storagerdquo IEEE Transactions on Energy Conversion Vol 16 No 1 pp 1 ndash 7 March 2001
[326] E S Abdin A M Osheiba and MM Khater ldquoModeling and optimal controllers design for a stand-alone photovoltaic-diesel generating unitrdquo IEEE Transactions on Energy Conversion Vol 14 No 3 pp 560-565 Sept 1999
[327] F Bonanno A Consoli A Raciti B Morgana and U Nocera ldquoTransient analysis of integrated diesel-wind-photovoltaic generation systemsrdquo IEEE Transactions on Energy Conversion Vol 14 No 2 pp 232-238 June 1999
[328] T Monai I Takano H Nishikawa and Sawada ldquoResponse characteristics and operating methods of new type dispersed power supply system using photovoltaic fuel cell and SMESrdquo 2002 IEEE PES Summer Meeting Vol 2 pp 874-879 2002
[329] F A Farret and M G Simotildees Integration of Alternative Sources of Energy John Wiley amp Sons Inc 2006
[330] Oslashystein Ulleberg ldquoStand-Alone Power Systems for the Future Optimal Design Operation amp Control of Solar-Hydrogen Energy Systemsrdquo PhD Dissertation Norwegian University of Science and Technology Trondheim 1998
[331] P Strauss A Engler ldquoAC coupled PV hybrid systems and microgrids-state of the art and future trendsrdquo Proceedings 3rd World Conference on Photovoltaic Energy Conversion Vol 3 No 12-16 pp 2129 ndash 2134 May 2003
[332] G Hegde P Pullammanappallil C Nayar ldquoModular AC coupled hybrid power systems for the emerging GHG mitigation products marketrdquo Proceedings Conference on Convergent Technologies for Asia-Pacific Region Vol 3 No15-17 pp 971 ndash 975 Oct 2003
[333] SK Sul I Alan and TA Lipo ldquoPerformance testing of a high frequency link converter for space station power distribution systemrdquo Proceedings the 24th Intersociety Energy Conversion Engineering Conference (IECEC-89) Vol 1 No 6-11 pp 617 ndash 623 Aug 1989
88
[334] H J Cha and P N Enjeti ldquoA three-phase ACAC high-frequency link matrix converter for VSCF applicationsrdquo Proceedings IEEE 34th Annual Power Electronics Specialist Conference 2003 (PESC 03) Vol 4 No 15-19 pp 1971 ndash 1976 June 2003
[335] R H Lasseter ldquoMicroGridsrdquo Proceedings 2002 IEEE PES Winter Meeting Vol 1 pp 305-308 2002
[336] IEEE Std 1547 IEEE Standard for Interconnecting Distributed Resources with Electric Power Systems 2003
[337] J Cahill K Ritland W Kelly ldquoDescription of Electric Energy Use in Single Family Residences in the Pacific Northwest 1986-1992rdquo Office of Energy Resources Bonneville Power Administration December 1992 Portland OR
89
CHAPTER 4
COMPONENT MODELING FOR THE HYBRID
ALTERNATIVE ENERGY SYSTEM
In this chapter the models for the main components of the proposed hybrid
alternative energy system given in Chapter 3 are developed Namely they are fuel cells
wind energy conversion system PV energy conversion system electrolyzer battery
power electronic interfacing circuits and accessory devices
Two types of fuel cells are modeled and their applications are discussed in this
dissertation They are low temperature proton exchange membrane fuel cell (PEMFC)
and high temperature solid oxide fuel cell (SOFC)
Dynamic Models and Model Validation for PEMFC
Introduction
PEMFCs show great promise for use as distributed generation (DG) sources
Compared with other DG technologies such as wind and photovoltaic (PV) generation
PEMFCs have the advantage that they can be placed at any site in a distribution system
without geographic limitations to achieve optimal performance Electric vehicles are
another major application of PEMFCs The increased desire for vehicles with less
emission has made PEMFCs attractive for vehicular applications since they emit
essentially no pollutants and have high power density and quick start
PEMFCs are good energy sources to provide reliable power at steady state but they
90
cannot respond to electrical load transients as fast as desired This is mainly due to their
slow internal electrochemical and thermodynamic responses The transient properties of
PEMFCs need to be studied and analyzed under different situations such as electrical
faults on the fuel cell terminals motor starting and electric vehicle starting and
acceleration
Some work has been reported in the literature on steady state fuel cell modeling eg
[41]ndash[47] as well as dynamic modeling [48]ndash[411] These studies are mostly based on
empirical equations andor electrochemical reactions inside the fuel cell In recent years
attempts have been made to study dynamic modeling of fuel cells with emphasis on the
electrical terminal characteristics eg [412]ndash[416] A detailed explanation of the
electrochemical properties of fuel cells and a simple equivalent electrical circuit
including a capacitor due to the double-layer charging effect inside fuel cells are reported
in [417]
In this dissertation dynamic models are presented for PEMFCs using electrical
circuits First through mechanistic analysis the equivalent internal voltage source and
equivalent resistors for activation loss ohmic voltage drop and concentration voltage
drop are given Then the double-layer charging effect is considered by adding an
equivalent capacitor to the circuit The thermodynamic characteristic inside the fuel cell
is also integrated into the model according to the energy balance equation A dynamic
model is built in MATLABSIMULINKreg and an electrical model is developed in Pspicereg
using equivalent electrical components from an electrical engineerrsquos point of view
Simulation results are given and validated with experimental data both for steady-state
and transient responses of PEMFCs The models show great potential to be useful in
91
other related studies such as real-time control of fuel cells and hybrid alternative energy
systems
Dynamic Model Development
In this section a mathematical approach is presented for building a dynamic model for
a PEMFC stack To simplify the analysis the following assumptions are made [41]
[45] [48] [417] [418]
(1) One-dimensional treatment
(2) Ideal and uniformly distributed gases
(3) Constant pressures in the fuel cell gas flow channels
(4) The fuel is humidified H2 and the oxidant is humidified air Assume the effective
anode water vapor pressure is 50 of the saturated vapor pressure while the
effective cathode water pressure is 100
(5) The fuel cell works under 100 ˚C and the reaction product is in liquid phase
(6) Thermodynamic properties are evaluated at the average stack temperature
temperature variations across the stack are neglected and the overall specific heat
capacity of the stack is assumed to be a constant
(7) Parameters for individual cells can be lumped together to represent a fuel cell
stack
A schematic diagram of a PEMFC and its internal voltage drops are shown in Figure
41
92
Gas Diffusion in the Electrodes In order to calculate the fuel cell output voltage
the effective partial pressures of H2 and O2 need to be determined In a gas mixture
consisting of N species the diffusion of component i through the porous electrodes can
be described by the Stefan-Maxwell formulation [41] [45]
sum=
minus=nabla
N
j ji
ijji
iD
NxNx
P
RTx
1
(41)
where xi (xj) = Mole fractions of species i (j)
Dij = effective binary diffusivity of i-j pair (m2s)
Ni(Nj) = Superficial gas flux of species i (j) [mol(m2middots)]
R = gas constant 83143 J(molmiddotK)
T = gas temperature (K)
P = overall pressure of the gas mixture (Pa)
93
Gas
Flow
Channel
Anode
Electrode
Cathode
Electrode
Membrane
Catalyst
Layers
H2O
H2
H2O
O2
N2
CO2
H+
0x
Vout
E
aohmV
membraneohmV
actV
concV
cohmV
Load
e- e-
Gas
Flow
Channel
Figure 41 Schematic diagram of a PEMFC and voltage drops across it
In the anode channel the gas stream is a mixture of H2 and H2O(g) The molar flux of
water (in gas phase) normal to anode surface OHN 2 can be set to zero according to
assumptions (1) ndash (3)
In the one-dimensional transport process along the x axis shown in Figure 41 the
diffusion of water can be simplified as
=
minus=
22
22
22
22222
HOH
HOH
aHOH
OHHHOH
a
OH
D
Nx
P
RT
D
NxNx
P
RT
dx
dx (42)
where Pa = overall gas pressure at the anode (Pa)
The molar flux of H2 can be determined by Faradayrsquos Law [41] [420]
94
F
IN den
H2
2 = (43)
where Iden = current density (Am2)
F = Faraday constant (96487 Cmol)
By combining (42) and (43) and integrating the expression with respect to x from the
anode channel to the catalyst surface it gives
=
22
2
22
expHOHa
adench
OHOHDFP
lRTIxx (44)
where la = distance from anode surface to the reaction site (m)
Superscript denotes the effective value
Superscript ldquochrdquo denotes the conditions at the anode or cathode channel
Since 1
2
2 =+ HOH xx the effective partial pressure of H2 is
)1(
2
2
2
2 OH
OH
OHH x
x
pp minus= (45)
According to assumption (4)
2OHp at the anode is sat
OHp 250 Therefore
2Hp is
given as [41]
minus
= 1
2exp
150
22
2
2
2
HOHa
adench
OH
sat
OHH
DFP
lRTIx
pp (46)
Superscript ldquosatrdquo denotes the condition of saturation
The gases flowing in the cathode channel are O2 N2 H2O(g) and CO2 Using (41) the
diffusion of H2O(g) at the cathode side can be obtained from
95
minus=
minus=
22
22
22
22222
OOH
OOH
cOOH
OOHOHO
c
OH
D
Nx
P
RT
D
NxNx
P
RT
dx
dx (47)
where Pc = overall gas pressure at the cathode (Pa)
Similar to the analysis for anode the effective molar fraction of water at the cathode
catalyst interface can be found as
=
22
2
24
expOOHc
cdench
OHOHDFP
lRTIxx (48)
where lc = distance from cathode surface to the reaction site (m)
Through similar analytical procedures [equations (47)-(48)] the effective molar
fraction of N2 and CO2 can also be determined
=
22
2
24
expONc
cdench
NNDFP
lRTIxx (49)
=
22
2
24
expOCOc
cdench
COCODFP
lRTIxx (410)
The effective molar fraction of O2 is
2
2
2
2 1 CONOHO xxxx minusminusminus= (411)
And the corresponding effective partial pressure of O2 is
)1(
2
2
2
2
2
2
2
2
2 CONOH
OH
OH
O
OH
OH
O xxxx
px
x
pp minusminusminus== (412)
According to assumption (4)
2OHp at the cathode equals sat
OHp 2 and the above
equation can be rewritten as
minus
minusminus= 1
1
2
2
22
2
OH
CONsat
OHOx
xxpp (413)
96
2Hp and
2Op calculated from (46) and (413) will be used in the Nernst equation to
find the fuel cell output voltage In the following subsection material balance equations
will be developed which will also be used to determine the fuel cell output voltage
Material Conservation Equations The instantaneous change in the effective partial
pressures of hydrogen and oxygen can be determined through the ideal gas equations as
follows [422]
F
iM
F
iMM
dt
dp
RT
VnetHoutHinH
Ha
22222
2 minus=minusminus= (414)
where Va = volume of anode channel (m3)
MH2 = H2 mole flow rate (mols)
i = fuel cell current (A)
Subscripts ldquoinrdquo ldquooutrdquo and ldquonetrdquo denote the values related to input output and
net
F
iM
F
iMM
dt
dp
RT
VnetOoutOinO
Oc
44222
2 minus=minusminus= (415)
where Vc = volume of cathode channel (m3)
MO2 = O2 mole flow rate (mols)
At steady-state all partial pressures are considered to be kept constant ie
0
2
2 ==dt
dp
dt
dp OH (416)
Therefore the net mole flow rates of H2 and O2 at steady-state are
F
IMM netOnetH
22 22 == (417)
Under transient state there are delays between the change in the load current and the
97
flow of fuel and oxidant The following relationships are used to represent these delay
effects
netO
netO
c
netH
netH
a
MF
i
dt
dM
MF
i
dt
dM
2
2
2
2
4
2
minus=
minus=
τ
τ (418)
where τa = fuel flow delay (s)
τc = oxidant flow delay (s)
Fuel Cell Output Voltage The overall reaction in a PEMFC can be simply written
as
)(2222
1lOHOH =+ (419)
According to assumption (5) the corresponding Nernst equation used to calculate the
reversible potential is [420]
[ ]50
2
20 )(ln2
OHcellcell ppF
RTEE sdot+= (420)
where Ecell = reversible potential of each cell (V)
E0cell is the reference potential which is a function of temperature and can be
expressed as follows [41]
)298(00 minusminus= TkEE E
o
cellcell (421)
where o
cellE 0= standard reference potential at standard state 298 K and 1atm pressure
To simplify the analysis a voltage Edcell is considered to be subtracted from the right
side of (420) for the overall effect of the fuel and oxidant delay The steady-state value
of Edcell is zero but it will show the influence of the fuel and oxidant delays on the fuel
98
cell output voltage during load transients It can be written as
[ ])exp()()( eecelld ttitiE τλ minusotimesminus= (422)
where λe = constant factor in calculating Ed (Ω)
τe = overall flow delay (s)
where ldquootimesrdquo is the convolution operator Converting (422) to the Laplace domain we get
1)()( +
=s
ssIsE
e
eecelld τ
τλ (423)
Equation (423) is used for developing models both in SIMULINK and Pspice The
internal potential Ecell in (420) now becomes
[ ] celldOHcellcell EppF
RTEE
50
2
20 )(ln2
minussdot+= (424)
Ecell calculated from (424) is actually the open-circuit voltage of the fuel cell
However under normal operating conditions the fuel cell output voltage is less than Ecell
Activation loss ohmic resistance voltage drop and concentration overpotential are
voltage drops across the fuel cell as shown in Figure 41 [418] Therefore
cellconccellohmcellactcellcell VVVEV minusminusminus= (425)
where Vcell = output voltage of a single cell (V)
Vactcell = activation voltage drop of a single cell (V)
Vohmcell = ohmic voltage drop of a single cell (V)
Vconccell = concentration voltage drop of a single cell (V)
Applying assumption 7) the output voltage of the fuel cell stack can be obtained as
concohmactcellcellout VVVEVNV minusminusminus== (426)
where Vout = output voltage of the fuel cell stack (V)
99
Ncell = number of cells in the stack (V)
Vact = overall activation voltage drop (V)
Vohm = overall ohmic voltage drop (V)
Vconc = overall concentration voltage drop (V)
To calculate the fuel cell output voltage the following estimations are used
1) Activation Voltage Drop Tafel equation given below is used to calculate the
activation voltage drop in a fuel cell [418]
[ ])ln()ln(0
IbaTI
I
zF
RTVact +sdot==
α (427)
On the other hand an empirical equation for Vact is given in [41] where a constant
(η0) is added to (427) as follows
210 )ln()298( actactact VVIbTaTV +=sdot+sdotminus+=η (428)
where η0 a b = empirical constants terms
Vact1=(η0+(T-298)middota) is the voltage drop affected only by the fuel cell internal
temperature while Vact2=(Tmiddotbmiddotln(I)) is both current and temperature dependent
The equivalent resistance of activation corresponding to Vact2 is defined as
I
IbT
I
VR actact
)ln(2 sdot== (429)
2) Ohmic Voltage Drop The ohmic resistance of a PEMFC consists of the resistance
of polymer membrane the conducting resistance between the membrane and electrodes
and the resistances of electrodes The overall ohmic voltage drop can be expressed as
ohmcohmmembraneohmaohmohm IRVVVV =++= (430)
ohmR is also a function of current and temperature [41]
100
TkIkRR RTRIohmohm minus+= 0 (431)
where Rohm0 = constant part of the Rohm
kRI = empirical constant in calculating Rohmic (ΩA)
kRT = empirical constant in calculating Rohmic (ΩK)
The values of kRI and kRT used in the simulation study are given in Table 43
3) Concentration Voltage Drop During the reaction process concentration gradients
can be formed due to mass diffusions from the flow channels to the reaction sites
(catalyst surfaces) At high current densities slow transportation of reactants (products)
to (from) the reaction sites is the main reason for the concentration voltage drop [418]
Any water film covering the catalyst surfaces at the anode and cathode can be another
contributor to this voltage drop [41] The concentration overpotential in the fuel cell is
defined as [418]
B
Sconc
C
C
zF
RTV lnminus= (432)
where CS is the surface concentration and CB is the bulk concentration
According to Fickrsquos first law and Faradayrsquos law [420] the above equation can be
rewritten as
)1ln(limit
concI
I
zF
RTV minusminus= (433)
where Ilimi = limitation current (A)
z = number of electrons participating
The equivalent resistance for the concentration loss is
101
)1ln(limit
concconc
I
I
zFI
RT
I
VR minusminus== (434)
Double-Layer Charging Effect In a PEMFC the two electrodes are separated by a
solid membrane (Figure 41) which only allows the H+ ions to pass but blocks the
electron flow [417] [418] The electrons will flow from the anode through the external
load and gather at the surface of the cathode to which the protons of hydrogen will be
attracted at the same time Thus two charged layers of opposite polarity are formed
across the boundary between the porous cathode and the membrane [417] [421] The
layers known as electrochemical double-layer can store electrical energy and behave
like a super-capacitor The equivalent circuit of fuel cell considering this effect is given
in Figure 42 which is similar to the circuit reported in [417] But the values of Ract [see
(429)] and the voltage source are different from what are defined in [417] Ract in [417]
is defined as VactI and the value of voltage source used in [417] is E
Figure 42 Equivalent circuit of the double-layer charging effect inside a PEMFC
In the above circuit C is the equivalent capacitor due to double-layer charging effect
Since the electrodes of a PEMFC are porous the capacitance C is very large and can be
in the order of several Farads [417] [426] Ract and Rconc are equivalent resistances of
102
activation and concentration voltage drops which can be calculated according to (429)
and (434) The voltage across C is
))(( concactC
C RRdt
dVCIV +minus= (435)
The double-layer charging effect is integrated into the modeling by using VC instead
of Vact2 and Vconc to calculate Vout The fuel cell output voltage now turns out to be
ohmCactout VVVEV minusminusminus= 1 (436)
Energy Balance of the Thermodynamics The net heat generated by the chemical
reaction inside the fuel cell which causes its temperature to rise or fall can be written as
losslatentsenselecchemnet qqqqq ampampampampamp minusminusminus= + (437)
where qnet = net heat energy (J)
qchem = Chemical or heat energy (J)
qelec = Electrical energy (J)
qloss = Heat loss (J)
The available power released due to chemical reaction is calculated by
Hnq consumedHchem ∆sdot= 2ampamp (438)
where ∆H = the enthalpy change of the chemical reaction inside the fuel cell
consumedHn 2
amp = H2 consumption rate (mols)
The maximum available amount of electrical energy is [418] [420]
[ ]50
2
20 )(ln OH ppRTGSTHG sdotminus∆=∆minus∆=∆ (439)
where ∆G = Gibbs free energy (Jmol)
103
∆G0 = Gibbs free energy at standard condition4 (Jmol)
∆S = entropy change (JmolmiddotK-1)
The electrical output power is computed as
IVq outelec sdot=amp (440)
The sensible and latent heat absorbed during the process can be estimated by the
following equation [48] [422]
( )( )
VgeneratedOH
lOHroomgeneratedOH
OroominOoutO
HroominHoutHlatentsens
Hn
CTTn
CTnTn
CTnTnq
sdot+
sdotminussdot+
sdotsdotminussdot+
sdotsdotminussdot=+
2
22
222
222
)(
amp
amp
ampamp
ampampamp
(441)
where qsens+latent = sensible and latent heat (J)
inamp = flow rate of species i (mols)
Ci = specific heat capacity of species i [J(molmiddotK)]
HV = Vaporization heat of water (Jmol)
Troom = room temperature (K)
The heat loss which is mainly transferred by air convection can be estimated by the
following formula [422]
cellcellroomcellloss ANTThq )( minus=amp (442)
where hcell = convective heat transfer coefficient [W(m2middotK)] It can be obtained through
experiments [48]
At steady state netqamp = 0 and the fuel cell operates at a constant temperature During
transitions the temperature of fuel cell will rise or drop according to the following
4 1atm 298K
104
equation [422]
netFCFC qdt
dTCM amp= (443)
where MFC is the total mass of the fuel cell stack and CFC is the overall specific heat
capacity of the stack
Dynamic Model Built in MatlabSimulink
A dynamic model for the PEMFC has been developed in MATLABSIMULINK
based on the electrochemical and thermodynamic characteristics of the fuel cell discussed
in the previous section The fuel cell output voltage which is a function of temperature
and load current can be obtained from the model Figure 43 shows the block diagram
based on which the MATLABSIMULINK model has been developed In this figure the
input quantities are anode and cathode pressures initial temperature of the fuel cell and
room temperature At any given load current and time the internal temperature T is
determined and both the load current and temperature are fed back to different blocks
which take part in the calculation of the fuel cell output voltage
105
Mass DiffusionEquations
Thermodynamic Equations
Nernst EquationActivation
Loss CalculationOhmic VoltageDrop Calculation
ConcentrationLoss Calculation
Double-layer Charging Effect
x
Vout
Pa
PcTroom
I
T
Load
Input Output Feedback
- -
+Tinitial
Material Conservation(Fuel amp Oxdiant Delay)
x+-
Figure 43 Diagram of building a dynamic model of PEMFC in SIMULINK
In this block diagram mass diffusion equations (41)-(413) are used to calculate the
effective partial pressures of H2 and O2 Then the Nernst equation (420) and the overall
fuel and oxidant delay effect given by (422) are employed to determine the internal
potential (E) of the fuel cell The ohmic voltage drop equations (430)-(431) activation
voltage drop equations (427)-(429) and concentration voltage drop equations
(433)-(434) together with the double-layer charging effect equation (435) are applied to
determine the terminal (output) voltage of the fuel cell Thermodynamic effects are also
considered via energy balance equations (437)-(443)
Equivalent Electrical Model in Pspice
In practice fuel cells normally work together with other electrical devices such as
power electronic converters Pspice is a valuable simulation tool used to model and
investigate the behavior of electrical devices and circuits An electrical equivalent model
of fuel cell built in Pspice can be used with electrical models of other components to
106
study the performance characteristics of the fuel cell power generation unit A block
diagram to build such model for PEMFC is given in Figure 44 which is also based on
the characteristics discussed previously The development of electrical circuit model for
different blocks in Figure 44 is discussed below
Internal Potential E According to (420)-(426) the internal potential E is a
function of load current and temperature An electrical circuit for the internal potential
block is given in Figure 45 The current and temperature controlled voltage source f1(IT)
in the figure represents the current and temperature dependent part of (420) Note that
the effective partial pressures (
2Hp and
2Op ) given in (420) are current dependent The
current controlled voltage source f2(I) stands for Edcell in (422)
[ ] )298()(ln2
)( 50
2
21 minus+sdotminus= TkNppF
RTNTIf EcellOH
cell (444)
celldcellENIf 2 )( = (445)
C
I
InternalPotential E
Activation Concentration
ThermodynamicBlockTroom
Tinitial
T
TT
Ohmic
T
T
Vout
Figure 44 Diagram of building an electrical model of PEMFC in Pspice
107
f1(IT)
oE0
f2(I)
E
I
Figure 45 Electrical circuit for internal potential E
Circuit for Activation Loss From (428) the activation voltage drop can be divided
into two parts Vact1 and Vact2 Vact1 can be modeled by a constant voltage source in series
with a temperature controlled voltage source Vact2 can be represented by a temperature
and current dependent resistor Ract This resistor is assumed to be composed of a
constant-value resistor (Ract0) a current-dependent resistor (Ract1) and a
temperature-dependent resistor (Ract2) A current-dependent resistor can be easily built in
Pspice by using the polynomial current controlled voltage source model ldquoHPOLYrdquo A
temperature-dependent resistor can be built by Analog Behavioral Models (ABMs) in
Pspice [424] The electrical circuit for activation voltage drop is given in Figure 46 In
this figure with reference to (428) we can write
Ract0
0η
f3(T)
Ract1
Ract2
I
Vact1
Vact2
Vact
Figure 46 Electrical circuit for activation loss
108
aTTf sdotminus= )298()(3 (446)
210 actactactact RRRR ++= (447)
Circuits for Ohmic and Concentration Voltage Drops According to (431) and
(434) both Rohm and Rconc are current and temperature dependent resistors Therefore
they can be modeled in Pspice the same way Ract is modeled Figure 47 shows the
equivalent circuit for ohmic voltage drop
210 ohmohmohmohm RRRR ++= (448)
Rohm0 is the constant part of Rohm With reference to (431) Rohm1=kRImiddotI is the
current-dependent part of Rohm and Rohm2 =-kRTmiddotT is its temperature-dependent part
Rohm0
Rohm1
Rohm2 I
Vohm
Figure 47 Electrical circuit for ohmic voltage drop
The electrical circuit model for concentration voltage drop is shown in Figure 48
210 concconcconcconc RRRR ++= (449)
where Rconc0 is the constant part of Rconc and Rconc1 Rconc2 are its current-dependent
and temperature-dependent parts
109
Rconc0
Rconc1
Rconc2 I
Vconc
Figure 48 Electrical circuit for concentration voltage drop
Equivalent Capacitor of Double-layer Charging Effect In Figure 44 C is the
equivalent capacitance of double-layer charging effect discussed in the previous section
This capacitance can be estimated through the measurement of the dynamic response of a
real fuel cell stack [417] Figure 42 shows how this capacitance is added into the circuit
Thermodynamic Block The analogies between the thermodynamic and electrical
quantities given in Table 41 are employed to develop the electrical circuit model for the
thermodynamic block shown in Figure 44 [423] The thermodynamic property inside the
fuel cell (437)-(443) can therefore be simulated by the circuit shown in Figure 49 The
power consumed by activation ohmic and concentration losses is considered as the heat
source which causes the fuel cell temperature to rise
IVEq outin sdotminus= )(amp (450)
The thermal resistance due to air convection is
)(1 cellcellcellT ANhR sdotsdot= (451)
In Figure 49 the constant voltage source ET represents the environmental
temperature and the voltage across the capacitance (Ch) is the overall temperature of the
fuel cell stack T
110
Environmental
Temperature
RT = Thermal Resistance
Ch = Heat Capacity
RT2 R
T2
Ch
inqamp
T
ET
Figure 49 Equivalent circuit of thermodynamic property inside PEMFC
TABLE 41 ANALOGIES BETWEEN THERMODYNAMIC AND ELECTRICAL QUANTITIES
Electrical Potential U (V) Temperature T(K)
Electrical Current I (A) Heat Flow Rate Ph (W)
Electrical Resistance R (Ohm) Thermal Resistance θ (KW)
Electrical Capacitance C (F) Heat Capacity Ch (JK)
URI = TθPh =
dt
dUCI =
dt
dTCP hh =
Model Validation
By applying the equations and the equivalent electrical circuits discussed in the
previous sections dynamic models for an Avista Labs (Relion now) SR-12 PEMFC stack
were built both in MATLABSIMULINK and Pspice environments The specifications of
SR-12 fuel cell stack are given in Table 42 [425] The electrical model parameter values
used in the simulation studies are listed in Table 43
111
TABLE 42 SPECIFICATIONS OF SR-12
Description Value
Capacity 500W
Number of cells 48
Operating environmental temperature 5degC to 35degC
Operating pressures PH2 asymp 15atm
Pcathode asymp 10atm
Unit Dimensions (WtimesDtimesH) 565times615times345 cm
Weight 44kg
The 9995 pure hydrogen flows at manifold pressure of about 7psi The
environmental air is driven by the SR-12rsquos internal fan to pass through the cathode to
provide oxygen
Experimental Setup To validate the models built in SIMULINK and Pspice real
input and output data were measured on the 500W SR-12 Avista Labs (Relion now)
PEMFC The block diagram of the experimental setup is shown in Figure 410 The
Chroma 63112 programmable electronic load was used as a current load Current signals
were measured by LEM LA100-P current transducers the output voltage was measured
by a LEM LV25-P voltage transducer and the temperature was measured by a k-type
thermocouple together with an analog connector The current voltage and temperature
data were all acquired by a 12-bit Advantech data acquisition card in a PC
112
TABLE 43 ELECTRICAL MODEL PARAMETER VALUES FOR SR-12 STACK
oE0 (V) 589 Ch (F) 22000
kE (VK) 000085 RT (Ω) 00347
τe (s) 800 C (F) 01F (48F for each cell)
λe (Ω) 000333 Rohm0 (Ω) 02793
η0 (V) 20145 Rohm1 (Ω) 0001872timesI
a (VK) -01373 Rohm2 (Ω) -00023712times(T-298)
Ract0 (Ω) 12581 Rconc0 (Ω) 0080312
Ract2 (Ω) 000112times(T-298) Rconc2 (Ω) 00002747times (T-298)
Ract1 (Ω) III
II
311600454501043
10223211067771
233
4456
minus+timesminus
times+timesminusminus
minusminus
Rconc1 (Ω) III
III
010542000555400100890
106437810457831022115
23
455668
minus+minus
times+timesminustimes minusminusminus
Chroma 63112
Programmable
Electronic Load
LEM LV25-P
Voltage
Transducer
LEM LA100-P
Current Transducer
Omega SMCJ
Thermocouple-to-
Analog Connector
PC with an Advantech PCI-1710
12-Bit Data Acquisition Card
K-Type
Thermocouple
SR-12
Internal
Circuit
SR-12
PEMFC
Stack
Istack
Iterminal
Figure 410 Experimental configuration on the SR-12 PEMFC stack
113
Steady-State Characteristics The steady state characteristics of SR-12 were
obtained by increasing the load current from 11A to 205A in steps of 02A every 40
seconds Both the stack current and terminal current (Figure 410) were measured but
only the stack current is used to validate the models since it is the current directly from
the fuel cell stack The experimental average value of V-I curve of the fuel cell is shown
in Figure 411 The steady-state responses of the models in SIMULINK and Pspice are
also given in Figure 411 in order to compare them with the experimental data Both the
SIMULINK and Pspice model responses agree very well with the real data from the fuel
cell stack The voltage drop at the beginning and end of the curves shown in Figure 411
are due to activation and concentration losses respectively The voltage drop in the
middle of the curves (which is approximately linear) is due to the ohmic loss in the fuel
cell stack [418]
Figure 412 shows the power vs current (P-I) curves of the PEMFC stack obtained
from the experimental data and the models The model responses also match well with
experimental data in this case Note that peak output power occurs near the fuel cell rated
output beyond which the fuel cell goes into the concentration zone In this region the
fuel cell output power will decrease with increasing load current due to a sharp decrease
in its terminal voltage
114
5 10 15 20 2522
24
26
28
30
32
34
36
38
40
Load Current (A)
PEMFC Output Voltage (V)
Average Value of the Measured DataResponse of the Model in SIMULINKResponse of the Model in Pspice
Upper range of the measured data
Lower range of the measured data
Figure 411 V-I characteristics of SR-12 and models
0 5 10 15 20 250
100
200
300
400
500
600
Load Current (A)
PEMFC Output Power (W)
Average Value of Measured DataModel in SIMULINKModel in Pspice
Lower range of the measured data
Upper range of the measured data
Figure 412 P-I characteristics of SR-12 and models
115
Temperature Response The temperature response of the PEMFC stack shown in
Figure 413 was measured under the same ramp load current as given in the previous
sub-section The temperature was measured as the current increased from 11A to 205A
with a slew rate of 5mAs The temperature response of the SIMULINK and Pspice
models are also given in Figure 413 for comparison with the measured values Although
there are some differences between the model responses and the measured data the
models can predict the temperature response of the fuel cell stack within 35K in the
worst case
0 500 1000 1500 2000 2500 3000 3500 4000306
308
310
312
314
316
318
320
Time (s)
Temperature Responses (K)
Measured Data
Model in SIMULINK
Model in Pspice
Figure 413 Temperature responses of the SR 12 stack and models
116
Transient Performance The dynamic property of PEMFC depends mainly on the
following three aspects double-layer charging effects fuel and oxidant flow delays and
thermodynamic characteristics inside the fuel cells Although the capacitance (C) due to
the double-layer charging effect is large (in the order of several Farads for each cell) the
time constant τ=(Ract+Rconc)middotC is normally small (less than 1 second) because (Ract+Rconc)
is small (less than 005Ω for the single cell used in this study) when the fuel cell works in
the linear zone Therefore capacitor C will affect the transient response of PEMFC in the
short time range The transient responses of the models to a fast step load change are
given in Figure 414 It is noted that when the load current steps up the voltage drops
simultaneously to some value due to the voltage drop across Rohm and then it decays
exponentially to its steady-state value due to the capacitance (C)
On the other hand the fuel and oxidant flows cannot follow the load current changes
instantaneously The delays can be in the range from several tens of seconds to several
hundreds of seconds Also the temperature of fuel cell stack cannot change
instantaneously The thermodynamic time constant of a PEMFC can be in the order of
minutes Thus the fuel and oxidant flow delays and the thermodynamic characteristics
will normally dominate the transient responses in the long time operation The
corresponding SIMULINK and Pspice model responses are given in Figure 415 From
this figure it is noticed that the voltage drops below its steady-state value when the load
steps up and then recovers back to its steady-state value in a relatively long time range (in
the order of about hundred seconds to several minutes) As shown in Figures 414 and
415 simulation results agree well with the measured data
117
209 2095 210 2105 211 2115 212 212526
28
30
32
34
36
38
Time (s)
Dynamic Responses in Short Time Range (V)
Measured DataModel in SIMULINKModel in Pspice
Model in Simulink
Model in Pspice
Measured Data
Figure 414 Transient responses of the models in short time range
400 600 800 1000 1200 1400 1600 1800 200026
28
30
32
34
36
38
Time (s)
PEMFC Dynamic Response (V)
Measured DataModel in SIMULINK
Model in Pspice
Measured Data Model in Pspice
Model in SIMULINK
Figure 415 Transient responses of the models in long time range
118
Dynamic Models for SOFC
Introduction
Solid oxide fuel cells are advanced electrochemical energy conversion devices
operating at a high temperature converting the chemical energy of fuel into electric
energy at high efficiency They have many advantages over conventional power plants
and show great promise in stationary power generation applications [427] [428] The
energy conversion efficiency of a SOFC stack can reach up to 65 and its overall
efficiency when used in combined heat and power (CHP) applications ie as an
integrated SOFC-combustion turbine system can even reach 70 [429] Despite slow
start-up and thermal stresses due to the high operating temperature SOFC allows for
internal reforming of gaseous fuel inside the fuel cell which gives its multi-fuel
capability [418] [430]
SOFC modeling is of interest for its performance prediction and controller design
Many SOFC models have been developed some are highly theoretical and are based on
empirical equations eg [431]-[433] and some are more application oriented
[434]-[437] Increased interest in SOFC power plant design and control has led to a
need for appropriate application oriented SOFC models An integrated SOFC plant
dynamic model for power system simulation (PSS) software was presented in [434]
Three operation limits of SOFC power plants were addressed in that paper in order to
achieve a safe and durable cell operation However the thermodynamic properties of
SOFCs were not discussed in the paper A transient model of a tubular SOFC consisting
of an electrochemical model and a thermal model was given in [435] However the
119
dynamic response of the model due to load variations was only investigated in large
(minute) time scale
In this section a dynamic model of a tubular SOFC stack is presented based on its
thermodynamic and electrochemical properties and on the mass and energy conservation
laws with emphasis on the fuel cell electrical (terminal) characteristics The SOFC model
implemented in MATLABSimulinkreg mainly consists of an electrochemical sub-model
and a thermodynamic sub-model The double-layer charging effect [439] is also taken
into account in the model The model responses are studied under both constant fuel flow
and constant fuel utilization operating modes The effect of temperature on the
steady-state V-I (output voltage vs current) and P-I (output power vs current)
characteristics are also studied The dynamic responses of the model are given and
discussed in different time scales ie from small time scale (10-3-10
-1 s) to large time
scale (102-10
3s) The temperature response of the model is given as well The SOFC
model has been used to study the SOFC overloading capability and to investigate the
performance of a SOFC distributed generation system which is reported in Chapters 5
and 6 The model shows the potential to be useful in SOFC related studies such as
real-time control of SOFC and its distributed generation applications
Dynamic Model Development
In this section a mathematical approach is presented for building a dynamic model for
a tubular SOFC fuel cell stack To simplify the analysis the following assumptions are
made
(1) One-dimensional treatment
120
(2) O= conducting electrolytes and ideal gases
(3) H2 fuel and large stoichiometric quantity of O2 at cathode
(4) H2 and O2 partial pressure are uniformly decreased along the anode channel while
the water vapor partial pressure is uniformly increased for normal operations
(5) Lumped thermal capacitance is used in the thermodynamic analysis and the
effective temperature of flowing gases in gas channels (anode and cathode
channels) is represented by its arithmetical mean value ( ) 2out
gas
in
gas
ch
gas TTT +=
(6) The combustion zone is not modeled in this SOFC thermal model The fuel and
air are assumed to be pre-heated
(7) Parameters for individual cells can be lumped together to represent a fuel cell
stack
A schematic diagram of a SOFC is shown in Figure 416 Two porous electrodes
(anode and cathode) are separated by a solid ceramic electrolyte This electrolyte material
(normally dense yttria-stabilized zirconia) is an excellent conductor for negatively
charged ions (such as O=) at high temperatures [418] At the cathode oxygen molecules
accept electrons from the external circuit and change to oxygen ions These negative ions
pass across the electrolyte and combine with hydrogen at the anode to produce water
For the details of principle of operation of SOFC the reader is referred to [418]
[427]-[429]
Effective Partial Pressures In this part expressions for H2 O2 and H2O partial
pressures at anode and cathode channels and their effective values at actual reaction sites
are derived in terms of the fuel cell operating parameters (eg fuel cell temperature fuel
121
and oxidant flow rates and anode and cathode inlet pressures) and the physical and
electrochemical parameters of the fuel cell These partial pressure values will be used to
calculate the fuel cell output voltage
Figure 416 Schematic diagram of a solid oxide fuel cell
As shown in Figure 416 when load current is being drawn H2 and O2 will diffuse
through the porous electrodes to reach the reaction sites and the reactant H2O will diffuse
from the reaction sites to the anode channel As a result H2 H2O and O2 partial pressure
gradients will be formed along the anode and cathode channels when the fuel cell is
under load Assuming uniform variation of gas partial pressures [assumption (4)] the
arithmetic mean values are used to present the overall effective gas partial pressures in
the channels
2
22
2
out
H
in
Hch
H
ppp
+= (452a)
122
2
22
2
out
OH
in
OHch
OH
ppp
+= (452b)
2
22
2
out
O
in
Och
O
ppp
+= (453)
The effective partial pressures of H2 and O2 at the actual reaction sites will be less
than those in the gas flow channels due to mass diffusion In contrast the vapor partial
pressure at reaction sites is higher than that in the anode flow channel In order to
calculate the fuel cell output voltage the effective partial pressures of H2 H2O and O2 at
the reaction sites need to be determined In a gas mixture consisting of N species the
diffusion of component i through the porous electrodes can be described by the
Stefan-Maxwell formulation [41]
sum=
minus=nabla
N
j ji
ijji
iD
NxNx
P
RTx
1
(454)
where xi (xj) = Mole fractions of species i (j)
Dij = effective binary diffusivity of i-j pair (m2s)
Ni(Nj) = Superficial gas flux of species i (j) [mol(m2middots)]
R = gas constant 83143 J(molmiddotK)
T = gas temperature (K)
P = overall pressure of the gas mixture (Pa)
In the anode channel the gas stream is a mixture of H2 and H2O In the
one-dimensional transport process along the x axis shown in Figure 416 the diffusion of
H2 can be simplified as
123
minus=
OHH
HOHOHH
ch
a
H
D
NxNx
P
RT
dx
dx
22
22222
(455)
The molar flux of H2 and H2O can be determined by Faradayrsquos Law [420]
F
iNN den
OHH222
=minus= (456)
Note that 122=+ OHH xx then (455) can be written as
F
i
D
RT
dx
dpden
OHH
H
222
2
minus= (457)
Similarly we can get the one-dimensional Stefan-Maxwell diffusion equation for
H2O
F
i
D
RT
dx
dpden
OHH
OH
222
2
= (458)
Integrating equations (457) and (458) with respect to x from the anode channel
surface to the actual reaction site will yield
den
OHH
ach
HH iFD
RTlpp
22
22
2minus= (459)
den
OHH
ach
OHOH iFD
RTlpp
22
22
2+= (460)
In the cathode channel the oxidant is air that mainly consists of O2 and N2 that is
122asymp+ NO xx Applying the same procedure as above the one-dimensional
Stefan-Maxwell diffusion equation for O2 can be expressed as
minus=
22
22222
NO
ONNO
ch
c
O
D
NxNx
P
RT
dx
dx (461)
124
Since nitrogen does not take part in the chemical reaction the net nitrogen molar flux
normal to the cathode surface can be set to zero
02=NN (462)
The molar flux of O2 is determined by Faradayrsquos Law
F
iN den
O42
= (463)
Equation (461) can now be rewritten as
)1(4 2
22
2
minus= O
NO
ch
c
denOx
DFP
RTi
dx
dx (464)
Similar to the analysis for the anode the effective partial pressure of oxygen at the
reaction site can be found as
( )
minusminus=
22
22
4exp
NO
ch
c
cdench
O
ch
c
ch
cODFP
lRTipPPp (465)
2Hp
2OHp and
2Op calculated from (459) (460) and (465) will be used in the
Nernst equation to find the fuel cell output voltage In the following subsection material
balance equations which will be also used to determine the fuel cell output voltage will
be developed
Material Conservation Equations The instantaneous change of the effective partial
pressures of hydrogen and water vapor in the anode gas flow channel can be determined
through the ideal gas equations as follows [422]
F
iMM
dt
dp
RT
V out
H
in
H
ch
Ha
222
2 minusminus= (466a)
125
F
iMM
dt
dp
RT
V out
OH
in
OH
ch
OHa
222
2 +minus= (466b)
F
iMM
dt
dp
RT
V out
O
in
O
ch
Oc
422
2 minusminus= (467)
Based on assumption (3) mass flow rate for H2 H2O and O2 at the inlet and outlet of
the flow channels can be expressed as
sdot=sdot=
sdot=sdot=
ch
a
out
H
a
out
Ha
out
H
ch
a
in
H
a
in
Ha
in
H
P
pMxMM
P
pMxMM
2
22
2
22
(468a)
sdot=sdot=
sdot=sdot=
ch
a
out
OH
a
out
OHa
out
OH
ch
a
in
OH
a
in
OHa
in
OH
P
pMxMM
P
pMxMM
2
22
2
22
(468b)
sdot=sdot=
sdot=sdot=
ch
c
out
O
c
out
Oc
out
O
ch
c
in
O
c
in
Oc
in
O
P
pMxMM
P
pMxMM
2
22
2
22
(469)
Rewriting (466) and (467) will give
iFV
RTp
PV
RTMp
PV
RTM
dt
dp
a
ch
Hch
aa
ain
Hch
aa
a
ch
H
2
2222
2 minusminus= (470a)
iFV
RTp
PV
RTMp
PV
RTM
dt
dp
a
ch
OHch
aa
ain
OHch
aa
a
ch
OH
2
2222
2 +minus= (470b)
iFV
RTp
PV
RTMp
PV
RTM
dt
dp
c
ch
Och
cc
cin
Och
cc
c
ch
O
4
2222
2 minusminus= (471)
Putting the above equations into Laplacersquos form we obtain
126
minus+
+= )(
4)0()(
)1(
1)(
222sI
FM
PPsP
ssP
a
ch
ach
Ha
in
H
a
ch
H ττ
(472a)
++
+= )(
4)0()(
)1(
1)(
222sI
FM
PPsP
ssP
a
ch
ach
OHa
in
OH
a
ch
OH ττ
(472b)
minus+
+= )(
8)0()(
)1(
1)(
222sI
FM
PPsP
ssP
ch
cch
Oc
in
O
c
ch
O ττ
(473)
where the time constant RTM
PV
a
ch
aaa
2=τ and
RTM
PV
c
ch
ccc
2=τ
The physical meaning of the time constant τa is that it will take τa seconds to fill a
tank of volume Va2 at pressure ch
aP if the mass flow rate is Ma Similar physical
meaning holds for τc
Fuel Cell Output Voltage The overall reaction in a solid oxide fuel cell is [418]
)(222 22 gOHOH =+ (474)
where subscript ldquogrdquo indicates the product H2O is in gas form The corresponding Nernst
equation used to calculate the reversible potential is [418] [420]
sdot+=
2
2
0)(
)(ln
42
22
ch
OH
ch
O
ch
H
cellcellp
pp
F
RTEE (475)
E0cell is a function of temperature and can be expressed as [418]
)298(00 minusminus= TkEE E
o
cellcell (476)
where o
cellE 0 is the standard reference potential at standard state 298 K and 1atm
pressure
Ecell calculated from (475) is actually the open-circuit voltage of the fuel cell
127
However when the fuel cell is under load its output voltage is less than Ecell due to
activation loss ohmic resistance voltage drop and concentration overpotential [418]
[431] The output voltage of a cell can therefore be written as
cellconccellohmcellactcellcell VVVEV minusminusminus= (477)
Applying assumption (7) the output voltage of the fuel cell stack can be obtained as
concohmactcellcellout VVVEVNV minusminusminus== (478)
To calculate the fuel cell output voltage the above three voltage drops will be
calculated first
1) Activation Voltage Drop Action voltage loss is caused by an activation energy
barrier that must be overcome before the chemical reaction occurs The Butler-Volmer
equation is normally used to calculate the activation voltage drop [431]
minusminusminus
=RT
zFV
RT
zFVii actact )1(expexp0 ββ (479)
where i0 = apparent exchange current (A)
β = electron transfer coefficient
i0 is the apparent exchange current which is mainly a function of temperature [438]
[439]
)exp( 210 TkTki aa minussdotsdot= (480)
where ka1 ka2 are empirical constants
Under high activation condition the first term in (479) is much higher than the
second term and the well-known Tafel equation can be obtained from (479) by
neglecting its second term [418] thus
128
=
0
lni
i
Fz
RTV cellact β
(481)
Equation (481) will yield an unreasonable value for Vact when i = 0 According to
[438] the value of β is about 05 for fuel cell applications and (479) can be written as
= minus
0
1
2
sinh2
i
i
zF
RTV cellact (482)
The equivalent activation resistance can then be defined as
== minus
0
1
2
sinh2
i
i
zFi
RT
i
VR
cellact
cellact (483)
According to (482) the activation voltage drop will be zero when load current is
zero The ohmic and concentration voltage drops (discussed in the next two sub-sections)
are also zero when the fuel cell is not loaded (i=0) However even the open-circuit
voltage of a SOFC is known to be less than the theoretical value given by (75) [417]
Similar to the computation of activation voltage of a proton exchange membrane fuel cell
[41] a constant and a temperature-dependent term can also be added to (482) for
activation voltage drop computation of SOFC as follows
cellactcellactcellactcellact VViRTV 1010 +=++= ξξ (484)
where ξ0 = constant term of activation voltage drop (V)
ξ1 = temperature coefficient of second term in activation voltage drop (VK)
TV cellact 100 ξξ += is the part of activation drop affected only by the fuel cell internal
temperature while cellactcellact iRV 1 = is both current and temperature dependent
2) Ohmic Voltage Drop The ohmic resistance of a SOFC consists mainly of the
resistance of the electrolyte electrodes and interconnection between fuel cells In this
129
model only ohmic losses of electrolyte and interconnection are included while the
resistance of electrodes is neglected The overall ohmic voltage drop can be expressed as
cellohmintercohmelecytohmcellohm iRVVV =+= (485)
cellohmR normally decrease as temperature increases it can be expressed as [438]
interc
cell
intercintercelecyt
cell
elecytelecyt
cellohmA
Tba
A
TbaR δδ
)exp()exp( += (486)
3) Concentration Voltage Drop During the reaction process concentration gradients
can be formed due to mass diffusion from the flow channels to the reaction sites (catalyst
surfaces) The effective partial pressures of hydrogen and oxygen at the reaction site are
less than those in the electrode channels while the effective partial pressure of water at
the reaction site is higher than that in the anode channel At high current densities slow
transportation of reactants (products) to (from) the reaction site is the main reason for the
concentration voltage drop [417] [418] The concentration overpotential in the fuel cell
can be obtained as
cconcaconc
OH
OH
ch
OH
ch
O
ch
H
cellconc
VV
p
pp
p
pp
F
RTV
2
2
2
2
)(
)(ln
)(
)(ln
42
22
2
22
+=
sdotminus
sdot=
(487)
minus
+=
)2()(1
)2()(1ln
2222
222
ch
HHOHdena
ch
OHHOHdena
aconcpFDiRTl
pFDiRTl
F
RTV (488)
minusminusminus=
22
2
2
4
exp)(1
ln4 NO
ch
c
cdench
O
ch
c
ch
cch
O
cconcDFp
lRTippp
pF
RTV (489)
The equivalent resistance for the concentration voltage drop can be calculated as
130
i
VR
cellconc
cellconc
= (490)
4) Double-layer charging effect In a SOFC the two electrodes are separated by the
electrolyte (Figure 416) and two boundary layers are formed eg anode-electrolyte layer
and electrolyte-cathode layer These layers can be charged by polarization effect known
as electrochemical double-layer charging effect [417] during normal fuel cell operation
The layers can store electrical energy and behave like a super-capacitor The model for
SOFC considering this effect can be described by the equivalent circuit shown in Figure
417 [417] [444]
Figure 417 Equivalent electrical circuit of the double-layer charging effect inside a
SOFC
In the above circuit Rohmcell Ractcell and Rconccell are equivalent resistances of ohmic
voltage drop activation and concentration voltage drops which can be calculated
according to (486) (483) and (490) respectively C is the equivalent capacitance of the
double-layer charging effect Since the electrodes of a SOFC are porous the value of C is
large and can be in the order of several Farads [417] The voltage across C is
))((
cellconccellact
cellC
cellC RRdt
dVCiV +minus= (491)
131
The double-layer charging effect is integrated into the modeling by using VCcell
instead of Vact1cell and Vconccell to calculate Vcell The fuel cell output voltage now turns
out to be
cellohmcellactcellCcellcell VVVEV 0 minusminusminus= (492)
Then (492) and (478) can be used to calculate the output voltage Vout of a SOFC
stack
Energy Balance of the Thermodynamics The cross section profile and heat transfer
inside a tubular SOFC are shown in Figure 418 [418] [440] One advantage of this
tubular structure is that it eliminates the seal problems between cells since the support
tube of each cell is closed at one end [418] The air is fed through a central air supply
tube (AST) and forced to flow back past the interior of the cell (cathode surface) to the
open end The fuel gas flows past the exterior of the cell (anode surface) and in parallel
direction to the air [418]
The thermal analysis for fuel reformer and combustor are not included in this model
Heat exchanges between cells are also not considered in this model by assuming that
temperature differences between adjacent cells can be neglected Heat transport inside the
fuel cell occurs mainly by means of radiation convection and mass flow
The heat generated by the chemical reaction inside the fuel cell can be written as
elecchemgen qqq ampampamp minus= (493)
The available power released due to chemical reaction is calculated by
Hnq consumedHchem ∆sdot= 2ampamp (494)
where ∆H is the enthalpy change of the chemical reaction inside the fuel cell
132
The real electrical output power is
iVq outelec sdot=amp (495)
Air Air Supply Tube
Fuel Cell
Fuel Cell
Fuel
Fuel
qgen
qconvinner
qconvann
qflowairAST
qflowairann q
rad
qfuel conv q
fuel flow
qconvouter
Figure 418 Heat transfer inside a tubular solid oxide fuel cell
The thermodynamic and energy balance analysis for different parts inside the cell are
discussed below [422] [440]
1) Cell Tube
elecchemgencellin qqqq ampampampamp minus== (496a)
fuelflowfuelconvannairflowannconvradcellout qqqqqq ampampampampampamp ++++= (496b)
dt
dTCmqqq cell
cellcellcelloutcellincellnet =minus= ampampamp (496c)
)( 44
ASTcellouterASTASTrad TTAq minus= σεamp (496d)
)( annaircellinnercellcellannconv TTAhq minus=amp (496e)
( )annairoutannairinairairmwairannairflow TTCMMq minus=amp (496f)
133
)( fuelcelloutercellcellfuelconv TTAhq minus=amp (496g)
OHflowHflowfuelflow qqq22
ampampamp += (496h)
22222 ))(( HmwH
in
fuel
out
fuel
out
H
in
HHflow MCTTMMq minus+=amp (496i)
OHmwOH
in
fuel
out
fuel
out
OH
in
OHOHflow MCTTMMq22222 ))(( minus+=amp (496j)
2) Fuel
fuelflowfuelconvfuelin qqq ampampamp += (497a)
fuelflowfuelout qq ampamp = (497b)
dt
dTCmqqq
fuel
fuelfuelfueloutfuelinfuelnet =minus= ampampamp (497c)
3) Air between Cell and Air Supply Tube (AST)
annairflowanncellconvannairin qqq ampampamp += (498a)
annairflowannairout qq ampamp = (498b)
dt
dTCmqqq
annair
airannairannairoutannairinannairnet
=minus= ampampamp (498c)
4) Air Supply Tube
outerASTconvradASTin qqq ampampamp += (499a)
ASTairflowinnerASTconvASTout qqq ampampamp += (499b)
dt
dTmCqqq AST
ASTASTASToutASTinASTnet =minus= ampampamp (499c)
)( ASTcellairouterASTouterASTouterASTconv TTAhq minus=amp (499d)
134
)( ASTairASTinnerASTinnerASTinnerASTconv TTAhq minus=amp (499e)
( )ASTairoutASTairinairairASTflowair TTCMq minus=amp (499f)
5) Air in AST
ASTairflowinnerASTconvASToutASTairin qqqq ampampampamp +== (4100a)
ASTairflowASTairout qq ampamp = (4100b)
dt
dTmCqqq
ASTair
ASTairairASTairoutASTairinASTairnet
=minus= ampampamp (4100c)
The symbols in the above equations (493-4100) are defined as
m = mass (kg)
Ci = specific heat capacity of species i [J(molmiddotK) or J(kgmiddotK)]
h = heat transfer coefficient [W(m2middotK)]
A = area (m2)
Mi = mole flow rate of species i (mols)
Mmw i = molecular weight of species i (kgmol)
ε = emissivity
σ = Stefan-Boltzmann constant 56696times10-8 Wm-2K-4
The superscripts and subscripts in the above equations are defined as
air Conditions for air
ann Annulus of cell
AST Air supply tube
cell Conditions for a single cell
135
ch Conditions at the anode or cathode channel
chem Chemical
conv Convective
conc Concentration
consumed Material consumed in chemical reaction
gen Material (energy) generated in chemical reaction
flow Flow heat exchange
Fuel Conditions for fuel
H2 Hydrogen
H2O Water
in Conditions of inputinlet
innerouter Innerouter conditions
mw Molecular weight (kgmol)
net Net values
O2 Oxygen
out Output
rad Radiation
Effective value
The thermal model of SOFC will be developed according to (493)-(4100)
Dynamic SOFC Model Implementation A dynamic model for a 5kW SOFC has
been developed in MATLABSimulink based on the electrochemical and thermodynamic
136
characteristics of the fuel cell discussed in the previous section The output voltage of the
fuel cell depends on conditions including fuel composition fuel flow oxidant flow
anode and cathode pressures cell temperature load current and the electrical and thermal
properties of the cell materials Figure 419 shows the block diagram based on which the
model has been developed In this figure the input quantities are anode and cathode
pressures (Pa and Pc) H2 flow rate (MH2) H2O flow rate (MH2O) air flow rate (Mair)
and initial temperature of the fuel cell and air (Tfuelinlet and Tairinlet) At any given load
current and time the cell temperature Tcell is determined and both the load current and
temperature are fed back to different blocks which take part in the calculation of the fuel
cell output voltage
In this block diagram material conservation equations (466)-(473) are used to
calculate the partial pressures of H2 H2O and O2 in flow channels Then the Nernst
equation (475) is employed to determine the internal potential (E) of the fuel cell
Diffusion equations (454)-(465) and the material conservation equations will give the
concentration loss of the cell The ohmic voltage drop is determined by (485) and
activation voltage is computed from (484) Eventually the terminal (output) voltage of
the fuel cell is determined by (478) and (492) and the double-layer charging effect
(491) The thermal model is developed via energy balance equations (493)-(4100)
137
Model Responses under Constant Fuel Flow Operation
Both the steady-state and dynamic responses of the SOFC model under constant flow
operating mode are given in this section The thermodynamic response of the model and
the impact of the operating temperature are also given The dynamic responses of the
model are investigated in different time scales
ch
gasP
gasP
Figure 419 Diagram of building a dynamic model of SOFC in SIMULINK
Steady-State Characteristics The steady-state terminal voltage vs current (V-I)
curves of the SOFC model at different temperatures are shown in Figure 420 These
curves are similar to the real test data reported in [418] [442] The activation voltage
drop dominates the voltage drop in the low-current region As load current increases the
ohmic voltage drop increases fast and becomes the main contribution to the SOFC
voltage drop When the load current exceeds a certain value (140A for this SOFC model)
the fuel cell output voltage will drop sharply due to large ohmic and concentration
voltage drops inside SOFC The variations of the above three voltage drops vs load
138
current at three different temperatures are shown in Figure 421
Figure 420 shows the effect of temperature on the SOFC V-I characteristic curve
The SOFC output voltage is higher at lower temperature in the low current zone while the
voltage is higher at higher temperature in the high current region These simulation
results showing the effect of temperature on SOFC performance are also similar to the
test data given in [418] and [442] The negative temperature coefficient of the
open-circuit internal potential E0cell defined by (476) and the temperature-dependent
activation voltage drop and ohmic voltage drop (shown in Figure 421) are the main
reasons for this kind of temperature dependent performance of the SOFC model As
shown in Figure 421 both the activation and ohmic voltage drops decrease as the fuel
cell temperature increases
0 50 100 1500
20
40
60
80
100
120
Load current (A)
SOFC output voltage (V)
1073K
1173K
1273K
Figure 420 V-I characteristics of the SOFC model at different temperatures
The corresponding output power vs current (P-I) curves of the model at different
139
temperatures are shown in Figure 422 At higher load currents (I gt 40 A) higher output
power can be achieved at higher operating temperatures Under each operating
temperature there is a critical load current point (Icrit) where the model output power
reaches its maximum value For example Icrit is 95 A at 1073 K 110 A at 1173 K and
120 A at 1273 K Beyond these points an increase in the load current will reduce the
output power due to large ohmic and concentration voltage drops
0 50 100 1500
10
20
30
40
50
Load current (A)
Voltage drops (V)
Figure 421 Three voltage drops at different temperatures
140
0 50 100 1500
1
2
3
4
5
6
7
Load current (A)
SOFC output power (kW)
Pa = 3atm Pc = 3atm Fuel 90H
2+10H
2O
Constant Flow (0096mols) Oxidant Air(6 Stoichs O
2)
1073K
1173K
1273K
Figure 422 P-I characteristics of the SOFC model at different temperatures
Dynamic Response The dynamic response of the SOFC model is mainly dominated
by the double-layer charging effect the time constants τa and τc [defined in (472) and
(473)] and the thermodynamic property of the fuel cell Although the capacitance (C) of
the double-layer charging effect is large (in the order of several Farads) the time constant
τdlc=(Ractcell+Rconccell)C is normally small (in the order of around 10-2 s) because
(Ractcell+Rconccell) is small (less than 20 mΩ for a single cell used in this study) when the
fuel cell works in the linear zone Therefore capacitor C will only affect the model
dynamic response in small time scale ie 10-3-10
-1 s The operating conditions of the
SOFC model for this simulation study are listed in Table 44 Figure 423 shows the
model dynamic responses in this small time scale under step current changes The load
current steps up from 0 A to 80 A at 01s and then steps down to 30 A at 02 s The lower
part of the figure shows the corresponding SOFC output voltage responses with different
141
capacitance values for the double-layer charging effect When the load current steps up
(down) the fuel cell output voltage drops down (rises up) immediately due to the ohmic
voltage drop Then the voltage drops (rises) ldquosmoothlyrdquo to its final value It is noted that
the larger is the capacitance C the slower the output voltage reaches its final value
because the larger is the effective time constant τdlc
0 005 01 015 02 025 030
50
100
Load current (A)
0 005 01 015 02 025 0360
70
80
90
100
110
Time (s)
SOFC output voltage (V)
C=4F
C=15F
C=04F
Fuel 90 H2 + 10 H
2O
Constant flow 0096 molsOxidant Air (6 Stoichs O
2)
Figure 423 Model dynamic responses with different equivalent capacitance values for
double-layer charging effect in small time scale
TABLE 44 OPERATING CONDITIONS FOR THE MODEL DYNAMIC RESPONSE STUDIES
Temperature (K) 1173
Anode input pressure (atm) 3
Cathode input pressure (atm) 3
Anode H2 flow rate (mols) 00864
Anode H2O flow rate (mols) 00096
Oxidant Air (6 stoichs O2)
142
Time constants τa and τc are in the order of 10-1-10
0 s for the model parameters used
in this dissertation They mainly affect the model dynamic responses in the time scale
10-1 to 10
1 s Figure 424 shows the model dynamic responses in this medium time scale
under the same type of step current changes as shown in Figure 423 The load current
steps up from 0 A to 80 A at 1s and then steps down to 30 A at 11s The operating
conditions of the model are the same as given in Table 44 except for the operating
pressures Figure 424 shows the SOFC output voltage responses under different
operating pressures (Pa = Pc = P) Higher operating pressure gives higher output voltage
and also increases time constants τa and τc [see (472) and (473)] shown in the figure
0 5 10 15 200
50
100
Load current (A)
0 5 10 15 2060
70
80
90
100
110
Time (s)
SOFC output voltage (V)
P=1atm
P=3atmP=9atm
Fuel 90 H2 + 10 H
2O
Constant flow 0096 molsOxidant Air (6 Stoichs O
2)
Figure 424 Model dynamic responses under different operating pressures in medium
time scale
The equivalent thermodynamic time constant of a SOFC can be in the order of tens of
minutes [440] [443] Thus for large time scale (102-10
3 s) the thermodynamic
characteristic will dominate the model dynamic responses Figure 425 shows the
143
transient response of the SOFC model under load changes The model was subjected to a
step change in the load current from zero to 100 A at 10 min and then the current drops
back to 30 A at 120 min The operating conditions are also the same as given in Table 44
except for the varying fuel cell operating temperatures The fuel and air inlet
temperatures are given in the figure When the load current steps up the SOFC output
voltage drops sharply and then rises to its final value When the load current steps down
the output voltage jumps up and then drops slowly towards its final value as shown in
Figure 425
0 50 100 150 200 2500
50
100
Load current (A)
0 50 100 150 200 25020
40
60
80
100
120
SOFC output voltage (V)
Time (Minute)
Figure 425 Model dynamic responses under different inlet temperatures in large time
scale
The corresponding temperature responses of the SOFC model are shown in Figure
426 From this figure the equivalent overall thermodynamic time constant of the model
is around 15 minutes
144
0 50 100 150 200 250950
1000
1050
1100
1150
1200
1250
1300
Time (Minute)
SOFC temperature (K)
Tinlet = 1073K
Tinlet = 1173K
Tinlet = 973K
Figure 426 Model temperature responses
Constant Fuel Utilization Operation
In the previous sections only constant flow operation for the SOFC model was
discussed The fuel cell can also be operated in constant fuel utilization mode in which
the utilization factor will be kept constant The utilization factor is defined as [418]
inHinH
consumedH
M
Fi
M
Mu
22
2 2== (4101)
The direct way to achieve constant utilization operation is to feed back the load
current with a proportional gain )2(1 uF times as shown in Figure 427 to control fuel flow
to the fuel processor As a result the input H2 will change as load varies to keep the fuel
utilization constant As shown in Figure 427 the fuel processor is modeled by a simple
delay transfer function )1(1 +sfτ τf is set to 5s in this dissertation
145
)(1 sf +τ
)2(1 uF times
Figure 427 Constant utilization control
In this section the fuel cellrsquos steady state characteristics and dynamic responses under
constant fuel utilization mode will be discussed The results will also be compared with
those obtained under constant flow operating mode The utilization factor is set for 085
(85 fuel utilization) for this study and other operating conditions are the same as listed
in Table 44 except the fuel and water flow rates that will change as the load current
changes
Steady-state Characteristics Figure 428 shows a comparison between the V-I
characteristic of the SOFC model with constant fuel utilization and constant fuel flow
operating modes The operating conditions for the constant flow operating mode are
listed in Table 44 For this specific study the output voltage under constant flow
operating mode is higher than that under constant utilization mode at the same load
current The voltage difference between the two operating modes keeps getting smaller as
the load current increases The reason for this is that the utilization factor of the constant
flow operation will be getting closer to the utilization factor (085) of the constant
utilization operation as load current increases The corresponding P-I curves also given
in Figure 428 show that the SOFC can provide more power under constant flow
146
operation
20 40 60 80 100 120 140 1600
20
40
60
80
100
120SOFC output voltage (V)
20 40 60 80 100 120 140 1600
1
2
3
4
5
6
Load current (A)
SOFC output power (kW)
Constant Flow
Constant Utilization
Pa = 3atm Pc = 3atmFuel 90H
2+10H
2O
T = 1173K
Figure 428 V-I and P-I characteristics of the SOFC model under constant fuel utilization
and constant fuel flow operating modes
Figure 429 shows the curves of input fuel versus load current for both operation
modes It shows that the constant flow operation mode requires more fuel input
especially at light loading But the unused H2 is not just wasted it can be used for other
purposes [440] or recycled to use again
147
20 40 60 80 100 120 1400
001
002
003
004
005
006
007
008
009
Load current (A)
Input H2 flow rate (mols)
Constant Flow
Constant Utilization
Figure 429 H2 input for the constant utilization and constant flow operating modes
Dynamic Responses Dynamic response of the SOFC model in small time scale is
dominated by the double-layer charging effect and in large time scale is mainly
determined by the thermodynamic properties of the fuel cell Both the double-layer
charging effect and the thermodynamic characteristics of the fuel cell are determined by
the fuel cellrsquos physical and electrochemical properties These properties are normally not
affected by whether the SOFC is operating under constant fuel flow mode or constant
fuel utilization mode However the dynamic response in medium time scale will be
affected by the operating mode since the fuel flow rate will change as load varies under
constant utilization operating mode This load-dependent fuel flow rate will give a
load-dependent time constant τa as well Therefore only the dynamic response in this
time scale will be discussed for the constant utilization operating mode
148
Figure 430 shows the model dynamic responses in the medium time scale under
similar step current changes used in the constant fuel flow operating mode The load
current steps up from 0 A to 80 A at 1s and then steps down to 30 A at 31 s The lower
part of Figure 430 shows the corresponding SOFC output voltage responses under
different operating pressures Similar to what is shown in Figure 424 for constant fuel
flow operating mode a higher operating pressure results in a higher output voltage and
larger time constants τa and τc [see (472) and (473)] In this case the dynamic responses
are not determined only by τa and τc but also by the dynamics of the fuel processor The
output voltage curves (Figure 430) show the typical characteristic of a second order
system while the dynamic responses in medium time scale for the constant flow operating
mode (Figure 424) exhibit the characteristic of a first order system Figure 230 shows
that the SOFC output voltage drops as the load current steps up undershoots and then
rises back to its final value While the load current steps down the voltage rises up
overshoots and then drops back to its final value We note that the fuel cell fails to start
up at 1 atm operating pressure due to the delay in the fuel processor which causes
insufficient fuel supply
The selection of a SOFC operating mode depends on the actual desired performance
requirements and is beyond the scope of this dissertation Only the constant fuel flow
operating mode will be studied in the following chapters
149
0 10 20 30 40 50 600
50
100
Load current (A)
0 10 20 30 40 50 6020
40
60
80
100
120
Time (s)
SOFC output voltage (V)
1atm
3atm
9atm
Fuel 90 H2 + 10 H
2O
T = 1173 KConstant utilizationOxidant Air (6 Stoichs O
2)
Starting failure at 1atm
Figure 430 Model dynamic responses under different operating pressures in medium
time scale with constant utilization operating mode
150
Wind Energy Conversion System
Introduction
Among the renewable energy technologies for electricity production wind energy
technology is the most mature and promising one The use of wind energy conversion
systems (WECS) is increasing world-wide (see Chapter 1) Moreover the economic
aspects of wind energy technology are promising enough to justify their use in stand
alone applications as well as grid connected operations
As wind velocity in an area changes continuously the energy available from it varies
continuously This necessitates a need for dynamic models of all systems involved which
are responsive to the changes in the wind to have a better understanding of the overall
system
Induction machines (usually squirrel cage rotor type) are often used for wind power
generation because of their ruggedness and low cost [445] However they are used
mostly in grid-connected operation because of their excitation requirement Induction
machines can be used in stand-alone applications provided that enough reactive
excitation is provided to them for self-excitation [446] [447] Induction generators can
cope with a small increase in the speed from rated value because due to saturation the
rate of increase of generated voltage is not linear with speed Furthermore self excited
induction generator (SEIG) has a self-protection mechanism because its output voltage
collapses when overloaded [448]-[451]
In this section modeling of variable speed wind energy conversion systems is
discussed A description of the proposed wind energy conversion system is presented and
151
dynamic models for both the SEIG and wind turbine are developed In addition the
effects of saturation characteristic on the SEIG are presented The developed models are
simulated in MATLABSimulink [457] Different wind and load conditions are applied
to the WECS model for validation purposes
System Configuration The configuration of the WECS system (Figure 431)
studied in this dissertation is similar to the system shown in Figure 25 (c) A SEIG
driven by a pitch controlled variable speed wind turbine acting as the prime mover is
used to generate electricity The output AC voltage (with variable frequency) of the SEIG
is rectified into DC and then a DCAC inverter is used to convert the DC into 60 Hz AC
For stand-alone operation an excitation compensating capacitor bank is necessary to start
the induction generator For grid-connected application the compensating capacitor bank
can be eliminated from the system However for a weak-grid the reactive power
consumed by the induction generator will deteriorate the situation It is better to have a
generation system with self starting capability Therefore for the wind energy system
studied in this dissertation an excitation capacitor bank is always added regardless of the
system being stand-alone or grid-connected
In this section only the modeling of the components inside the rectangle in Figure 4
31 is discussed The design and modeling of power electronic circuits are discussed later
in this chapter It is noted from the figure that there are two main components inside the
rectangle the wind turbine together with the gear box and the SEIG
152
Figure 431 System block diagram of the WECS
Dynamic Model for Variable Speed Wind Turbine
The following sections explain the modeling and the control principles of the variable
speed pitch controlled wind turbine
Wind Turbine Characteristics The power Pwind (in watts) extracted from the wind is
given in equation 251 It is rewritten here as
)(2
1 3 θλρ pwind CAvP = (4102)
where ρ is the air density in kgm3 A is the area swept by the rotor blades in m
2 v is
the wind velocity in ms Cp is called the power coefficient or the rotor efficiency and is
function of tip speed ratio (TSR or λ see equation 252) and pitch angle (θ) [464]
The maximum rotor efficiency Cp is achieved at a particular TSR which is specific to
the aerodynamic design of a given turbine The rotor must turn at high speed at high
wind and at low speed at low wind to keep TSR constant at the optimum level at all
153
times For operation over a wide range of wind speeds wind turbines with high tip speed
ratios are preferred [453]
In the case of the variable speed pitch-regulated wind turbines considered in this
dissertation the pitch angle controller plays an important role Groups of λCpminus curves
with pitch angle as the parameter obtained by measurement or by computation can be
represented as a nonlinear function [455] [456] [466] The following function is used
( ) )exp( 54321 CCCCCC p minusminusminus= θ (4103)
where θ is the pitch angle
Proper adjustment of the coefficients C1-C5 would result in a close simulation of a
specific turbine under consideration The values for C1-C5 used in this study are listed in
Table 45 The Cp-λ characteristic curves at different pitch angles are plotted in Figure
432 From the set of curves in Figure 432 we can observe that when pitch angle is equal
to 2 degrees the tip speed ratio has a wide range and a maximum Cp value of 035
suitable for wind turbines designed to operate over a wide range of wind speeds With an
increase in the pitch angle the range of TSR and the maximum value of power coefficient
decrease considerably
TABLE 45 PARAMETER VALUES FOR C1-C5
C1 05
C2 116kθ
C3 04
C4 5
C5 21kθ
154
kθ in Table 45 used to calculate C2 and C5 is determined by λ and θ as [455] [456]
[466]
1
3 1
0350
080
1minus
+
minus+
=θθλθk (4104)
0 2 4 6 8 10 12 14 16 18 200
005
01
015
02
025
03
035
04
045
05
TSR λ
Cp
0 deg
1 deg
2 deg
3 deg
4 deg5 deg
10 deg
15 deg
20 deg
30 deg
Figure 432 Cp-λ characteristics at different pitch angles (θ)
For variable speed pitch-regulated wind turbines two variables have direct effect on
their operation namely rotor speed and blade pitch angle [452]-[454] Power
optimization strategy is employed when wind speed is below the turbine rated wind
speed to optimize the energy capture by maintaining the optimum TSR Power limitation
strategy is used above the rated wind speed of the turbine to limit the output power to the
rated power This is achieved by employing a pitch angle controller which changes the
blade pitch to reduce the aerodynamic efficiency thereby reducing the wind turbine
power to acceptable levels as discussed in Chapter 2 The different regions of the
155
above-mentioned control strategies of a variable speed wind turbine system are as shown
in the Figure 433
Figure 433 Variable speed pitch controlled wind turbine operation regions
Pitch Angle Controller The pitch angle controller used in this study employs PI
controllers as shown in Figure 434 [452] [456] [466] These controllers control the
wind flow around the wind turbine blade thereby controlling the toque exerted on the
turbine shaft If the wind speed is less than the rated wind speed the pitch angle is kept
constant at an optimum value If the wind speed exceeds the rated wind speed the
controller calculates the power error (between the reference power and the output power
of the wind turbine) and the frequency error (between the measured stator electrical
frequency of the SEIG and the rated frequency) The output of the controllers gives the
required pitch angle (Figure 434) In this figure the Pitch Angle Rate Limiter block
limits the rate of change of pitch angle as most modern wind turbines consist of huge
rotor blades The maximum rate of change of the pitch angle is usually in the order of 3o
to 10osecond
156
Figure 434 Pitch angle controller
turbineω
λminuspC
genω
ratedω
Figure 435 Simulation model of the variable speed pitch-regulated wind turbine
157
Variable-speed Wind Turbine Model The dynamic model of the variable speed
wind turbine are developed in MATLABSimulink Figure 435 shows the block diagram
of the wind turbine model
The inputs for the wind turbine model are wind speed air density radius of the wind
turbine mechanical speed of the rotor referred to the wind turbine side and power
reference for the pitch angle controller The output is the drive torque Tdrive which drives
the electrical generator The wind turbine calculates the tip speed ratio from the input
values and estimates the value of the power coefficient from the performance curves The
pitch angle controller maintains the value of the blade pitch at optimum value until the
power output of the wind turbine exceeds the reference power input
Dynamic Model for SEIG
There are two fundamental circuit models employed for examining the characteristics
of a SEIG One is the per-phase equivalent circuit which includes the loop-impedance
method adapted by Murthy et al [459] and Malik and Al-Bahrani [460] and the nodal
admittance method proposed by Ouazene and Mcpherson [449] and Chan [461] These
methods are suitable for studying the machinersquos steady-state characteristics Another
method is the dq-axis model based on the generalized machine theory proposed by Elder
et al [448] and Grantham et al [450] and is employed to analyze both the machinersquos
transient as well as steady-state
Steady-state Model Steady-state analysis of induction generators is of interest both
from the design and operational points of view By knowing the parameters of the
158
machine it is possible to determine its performance at a given speed capacitance and
load conditions
Loop impedance and nodal admittance methods used for the analysis of SEIG are
both based on per-phase steady-state equivalent circuit of the induction machine (Figure
436) modified for the self-excitation case They make use of the principle of
conservation of active and reactive powers by writing proper loop equations [459]
[460] [465] or nodal equations [449] [461] for the equivalent circuit These methods
are very effective in calculating the minimum value of capacitance needed for
guaranteeing self-excitation of the induction generator For stable operation excitation
capacitance must be slightly higher than the minimum value Also there is a speed
threshold the cutoff speed of the machine below which no excitation is possible In the
following paragraph a brief description of the loop impedance method is given for better
understanding
The per-unit (pu) per-phase steady-state circuit of a self-excited induction generator
under lagging (RL) load is shown in Figure 436 [459] [449] In the analysis of SEIG
the following assumptions were made [459]
1 Only the magnetizing reactance Xm is assumed to be affected by magnetic
saturation and all other parameters of the equivalent circuit are assumed to be constant
Self-excitation results in the saturation of the main flux and the value of Xm reflects the
magnitude of the main flux Leakage flux passes mainly in the air and thus these fluxes
are not affected to any large extent by saturation of the main flux
159
2 Per unit values of the stator and rotor leakage reactance (referred to stator side)
are assumed to be equal (Xls = Xlr = Xl) This assumption is normally valid in induction
machine analysis
3 Core loss in the machine is neglected
Figure 436 Equivalent T circuit of self-excited induction generator with R-L Load
In the figure the symbols are
Rs Rr R pu per-phase stator rotor (referred to stator) and load resistance
respectively
Xl X Xm pu per-phase statorrotor leakage load and magnetizing reactances (at
base frequency) respectively
Xc pu per-phase capacitive reactance (at base frequency) of the terminal excitation
capacitor
f v pu frequency and speed respectively
Vg V0 pu per-phase air gap and output voltages respectively
For the circuit shown in Figure 436 the loop equation for the current can be written
as
160
I Z = 0 (4105)
where Z is the net loop impedance given by
+
minus+++
+
minus= jX
f
R
f
jXjX
f
RjXjX
vf
RZ c
l
s
ml
r
2 (4106)
For equation (4105) to hold true for any current I the loop impedance (Z) should be
zero This implies that both the real and imaginary parts of Z are zero These two
equations can be solved simultaneously for any two unknowns such as f and Xc
Self-excitation Process The process of self-excitation in induction machines has
been known for several decades [446] [447] When capacitors are connected across the
stator terminals of an induction machine driven by an external prime mover voltage will
be induced at its terminals The induced electromotive force (EMF) and current in the
stator windings will continue to rise until the steady state condition influenced by the
magnetic saturation of the machine is reached At this operating point the voltage will be
stabilized at a given value and frequency In order for self-excitation to occur for a
particular capacitance value there is a corresponding minimum speed [447] [458]
Therefore in stand-alone mode of operation it is necessary for the induction generator to
be operated in the saturation region This guarantees one and only one intersection
between the magnetization curve and the capacitor reactance line as well as output
voltage stability under load as seen in Figure 437 [445] [455]
Under no load the capacitor current cgc XVI = must be equal to the magnetizing
current mgm XVI = when the stator impedance (Rs + jXl) is neglected and the rotor
circuit can be considered as open circuit as shown in Figure 437 The stator phase
161
voltage Vg (Vg = V0 in this case) is a function of magnetizing current Im linearly rising
until the saturation point of the magnetic core is reached With the value of self exciting
capacitance equal to C the output frequency of the self-excited generator is
)π(21 mCXf =
ω
minus
C
1tan 1
Figure 437 Determination of stable operation of SEIG
Dynamic Model of SEIG in dq Representations The process of self-excitation is a
transient phenomenon and is better understood if analyzed using a transient model To
arrive at a transient model of an induction generator an abc-dq0 transformation is used
The dq axis model based on the generalized machine theory proposed by Elder
[448] Salama [458] and Grantham [450] is employed to analyze the machinersquos
transient state as well as steady state To arrive at a transient model of an induction
generator abc-dq0 transformation [462] has been used in this analysis
Figure 438 shows the dq axis equivalent circuit of a self excited induction generator
shown in Figure 436 in stationary reference frame [451] [458] [462]
162
drrλω
+
qsVmL
sr lrL + minus
qrrλωminus
+
minus
dsV mL
srlsL lrL
+ minus
minus
rr
rr
lsL
cqVLZ
cdVLZdsλ
drλ
qrλqsλ
+
minus
minus
+
Figure 438 dq representation of a SEIG (All values are referred to stator)
In the figure rω is the electrical angular velocity of the rotor s(r) subscript denotes
parameters and variables associated with stator (rotor) respectively Vcq (Vqs) and Vcd
(Vds) are q and d axis voltages respectively and iqs (ids) is the q (d) axis component of
stator current Iqr (idr) is the q (d) axis component of rotor current Lls Llr and Lm are stator
leakage rotor leakage and magnetizing inductances of the stator qsλ and dsλ are q and
d axis components of stator flux linkages qrλ and drλ are q and d axis components of
rotor flux linkages
From Figure 438 the equation for no-load operation of SEIG can be written as
shown below
163
+
+
minus+minus
++
++
=
d
q
cdo
cqo
dr
qr
ds
qs
rrrrmmr
rrrrmrm
mss
mss
K
K
V
V
i
i
i
i
pLrLωpLLω
LωpLrLωpL
pL0pC1pLr0
0pL0pC1pLr
0
0
0
0
(4107)
where p = ddt Kd (Kq) is a constant representing initial induced voltage along the d (q)
axis due to the remaining magnetic flux in the core Vcqo and Vcdo are initial q and d
component voltages across the capacitor and Ls=Lls+Lm Lr=Llr+Lm
Equation (4107) can be modified to obtain four first order differential equations as
BAIpI += (4108)
The mechanical system is described by
generdrive TpωP
2JT minus+
= (4109)
where
minusminusminus
minus
minus
minusminusminus
=
rsrrssmmrs
rrsrsmrssm
rmrrmssr
2
m
rrmrmr
2
msr
rLLωLrLLωL
LωLrLLωLrL
rLLωLrLωL
LωLrLωLrL
L
1A
minus
minus
minus
minus
=
dscdm
qscqm
cdrdm
cqrqm
KLVL
KLVL
VLKL
VLKL
L
1B
=
dr
qr
ds
qs
i
i
i
i
I 2
mrs LLLL minus= 0
0
1cq
t
qscq VdtiC
V += int and 0
0
1cd
t
dscd VdtiC
V += int
J - Inertia of the rotor in (Kgm2)
Tdrive ndash wind turbine torque in (Nm)
Te_gen ndash electromagnetic torque by the generator in (Nm)
P ndash number of poles
164
The simulation of the SEIG can be carried out by solving (4108) Since the
magnetization inductance Lm is nonlinear in nature an internal iteration has to be done at
each integration step Given the initial condition from the previous step the
magnetization current can be calculated as shown below [450]
22 )()( qrqsdrdsm iiiiI +++= (4110)
The variation of magnetizing inductance as a function of magnetizing current used in
this study is given by
Lm = 05times[0025+02974timesexp(-004878timesIm)] (4111)
Any combination of R L and C can be added in parallel with the self-excitation
capacitance to act as load For example if resistance R is added in parallel with the
self-excitation capacitance then the term 1pC in the matrix (see 4107) becomes
R(1+RpC) The load can be connected across the capacitors once the voltage reaches a
steady-state value [450] [451] If there is an inductive load connected across the
excitation capacitor it influences the effective value of excitation capacitance such that it
results in an increase in the slope of the straight line of the capacitive reactance (Figure
437) reducing the terminal voltage This phenomenon is more pronounced when the
load inductance gets higher in value A capacitor for individual compensation can be
connected across the terminal of the load in such a way that it follows the load
conditions [463]
Ratings of the induction machine simulated are given in Table 32 (Chapter 3) The
detailed parameters used in modeling the SEIG are given in Table 46 The parameters
are obtained from [462] based on the same pu values of a 500 hp 2300 V induction
165
machine
TABLE 46 SEIG MODEL PARAMETERS
rs 0164 Ω
rr 0117 Ω
Xls 0754 Ω
Xlr 0754 Ω
Lm See (4111)
J 1106 kgm2
C 240 microF
P (Number of poles) 4
All reactances are based on 60 Hz
Responses of the Model for the Variable Speed WECS
The model of a 50 kW variable speed wind energy conversion system consisting of a
pitch-regulated wind turbine and self excited induction generator is developed in
MATLABSimulink environment using SimPowersystems block-set In this sub-section
the model responses under different scenarios are discussed
Wind Turbine Output Power Characteristic Figure 439 shows the wind turbine
output power of the simulated model for different wind velocities It can be observed that
the output power is kept constant at higher wind velocities even though the wind turbine
has the potential to produce more power This is done to protect the electrical system and
to prevent the over speeding of the rotor
166
0 5 10 15 20 250
10
20
30
40
50
Wind Speed (ms)
Output Power (kW)
Figure 439 Wind turbine output power characteristic
Process of Self-excitation in SEIG The process of self-excitation can occur only if
there is some residual magnetism For numerical method of integration residual
magnetism cannot be zero at the beginning of the simulation Therefore non-zero initial
values are set for Kq [andor Kd see equation (4107)] and the rotor speed
The process of voltage build up continues starting with the help of the residual
magnetism until the iron circuit saturates and therefore the voltage stabilizes In other
terms the effect of this saturation is to modify the magnetization inductance Lm such that
it reaches a saturated value the transient then neither increases nor decreases and
becomes a steady state quantity giving continuous self-excitation The energy for the
above process is provided by the kinetic energy of the wind turbine rotor [450] Figure
440 shows the process of a successful self excitation in an induction machine under no
load condition with wind speed at 10ms The value of the excitation capacitor is given in
the figure An unsuccessful self excitation process under the same condition (except a
167
smaller capacitor bank) is shown in Figure 441
0 05 1 15 2 25 3-600
-400
-200
0
200
400
600
Time (s)
Terminal Voltage (V)
C = 240 microF
Figure 440 A successful self excitation process
0 1 2 3 4 5 6 7 8 9 10-60
-40
-20
0
20
40
60
Time (s)
Terminal Voltage (V)
C = 10 microF
Figure 441 Voltage fails to build up
168
Figures 442 and 443 show the variations in magnetizing current and magnetizing
inductance vs time for successful voltage build up of the SEIG From Figures 440 442
and 443 it can be observed that the phase voltage slowly starts building up and reaches a
steady state value as the magnetization current starts from zero and reaches a steady state
value Also we see that the self excitation follows the process of magnetic saturation of
the core and the stable output value is reached only when the machine core is saturated
0 05 1 15 2 25 30
10
20
30
40
50
Time (s)
Magnetizing Current Im (A)
Figure 442 Variation of magnetizing current Im
0 05 1 15 2 25 30
005
01
015
02
Time (s)
Magnetizing Inductance Lm (H)
Figure 443 Variation of magnetizing inductance Lm
169
Model Responses under Wind Speed Changes In this section the responses of the
model for the variable speed WECS to wind speed variations are given and discussed
The wind speed changes are shown in Figure 444 The wind speed used in simulation
steps up from 10 ms to 16 ms at t = 30 s and changes from 16 ms to 8 ms at 60 s
10 20 30 40 50 60 70 80
4
6
8
10
12
14
16
18
Time (s)
Wind Speed (ms)
Figure 444 Wind speed variations used for simulation study
10 20 30 40 50 60 70 800
10
20
30
40
50
60
Time (s)
Wind Power (kW)
Wind speed 10 ms
Wind speed 16 ms
Wind speed 8 ms
Figure 445 Output power of the WECS model under wind speed changes
170
Figure 445 shows the output power of the WECS The WECS starts to supply power
at 3 s It is noted from the figure that the output power is 162 kW at 10 ms wind speed
50 kW at 16 ms and 486 kW at 8 ms respectively This matches the system output
power characteristic shown in Figure 439
10 20 30 40 50 60 70 801200
1400
1600
1800
2000
2200
2400
2600
Time (s)
Rotor Speed (rpm)
Wind speed 10 ms
Wind speed 16 ms
Wind speed 8 ms
Figure 446 Wind turbine rotor speed
Figure 446 shows the wind turbine rotor speed under the wind speed changes The
rotor speed is a slightly under 1800 rpm (rated speed) when there is no load When the
load is connected at 3 s the speed drops to about 1430 rpm When the wind speed is
increased to 16 ms at 30 s there is a fast increase in rotor speed as shown in Figure
446 Then the pitch controller starts operating to bring the rotor speed down to 1890 rpm
which is the upper limit (+5) of the frequency regulation band in the pitch controller
(see Figure 434) The rotor speed drops to 1257 rpm as the wind speed drops to 8 ms at
60 s
171
Figure 447 shows how the pitch angle changes during the wind speed variation Note
that the pitch angle keeps at the optimum value (2˚ in this study) when the wind speed is
below the nominal value (14 ms) When the wind speed exceeds 14 ms (at 30 s) the
pitch controller begins to work and increases the pitch angle to about 615˚ to keep the
output power constant (at 50 kW) The corresponding Cp is shown in Figure 448
10 20 30 40 50 60 70 802
3
4
5
6
7
Time (s)
Pitch Angle (Degree)
Figure 447 Pitch angle controller response to the wind changes
0 10 20 30 40 50 60 70 800
01
02
03
04
Time (s)
Cp
Figure 448 Variation of power coefficient Cp
172
Solar Energy Conversion System
The principle of operation of a PV cell is discussed in Chapter 2 In this section
model development of a PV module is given in details The PV model developed for this
study is based on the research work reported in [467]-[470]
Modeling for PV CellModule
The most commonly used model for a PV cell is the one-diode equivalent circuit as
shown in Figure 449 [467]-[470] Since the shunt resistance Rsh is large it normally can
be neglected The five parameters model shown in Figure 449 (a) can therefore be
simplified into that shown in Figure 449 (b) This simplified equivalent circuit model is
used in this study
Figure 449 One-diode equivalent circuit model for a PV cell (a) Five parameters
model (b) Simplified four parameters model
The relationship between the output voltage V and the load current I can be expressed
as
minus
+minus=minus= 1exp0 α
s
LDL
IRUIIIII (4112)
173
where IL = light current (A)
I0 = saturation current (A)
I = load current (A)
U = output voltage (V)
Rs = series resistance (Ω)
α = thermal voltage timing completion factor (V)
There are four parameters (IL I0 Rs and α) that need to be determined before the I-U
relationship can be obtained That is why the model is called a four-parameter model
Both the equivalent circuit shown in Figure 449 (b) and the equation (4112) look simple
However the actual model is more complicated than it looks because the above four
parameters are functions of temperature load current andor solar irradiance In the
remainder of this section procedures are given for determining the four parameters
Light Current IL According to [468] and [469] IL can be calculated as
( )[ ]refccSCIrefL
ref
L TTIΦ
ΦI minus+= micro (4113)
where Φ = irradiance (Wm2)
Φref = reference irradiance (1000 Wm2 is used in this study)
ILref = light current at the reference condition (1000Wm2 and 25 ˚C)
Tc = PV cell temperature (˚C)
Tcref = reference temperature (25 ˚C is used in this study)
microISC = temperature coefficient of the short-circuit current (A˚C)
Both ILref and microISC can be obtained from manufacturer data sheet [469]
174
Saturation Current I0 The saturation current can be expressed in terms of its value
at the reference condition as [468]-[469]
+
+minus
+
+=
273
2731exp
273
273
3
00
c
refc
ref
sgap
c
refc
refT
T
q
Ne
T
TII
α (4114)
where I0ref = saturation current at the reference condition (A)
egap = band gap of the material (117 eV for Si materials)
Ns = number of cells in series of a PV module
q = charge of an electron (160217733times10-19 C)
αref = the value of α at the reference condition
I0ref can be calculated as
minus=
ref
refoc
refLref
UII
α
0 exp (4115)
where Uocref = the open circuit voltage of the PV module at reference condition (V)
The value of Uocref is provided by manufacturers The value calculation for α is
discussed in the next section
Calculation of α According to [469] the value of αref can be calculated as
minus+
minus
minus=
refsc
refmp
refmprefsc
refsc
refocrefmp
ref
I
I
II
I
UU
1ln
2α (4116)
where Umpref = maximum power point voltage at the reference condition (V)
Impref = maximum power point current at the reference condition (A)
Iscref = short circuit current at the reference condition (A)
175
α is a function of temperature which as expressed as
ref
refc
c
T
Tαα
273
273
+
+= (4117)
Series Resistance Rs Some manufacturers provide the value of Rs If not provided
the following equation can be used to estimate its value [469]
refmp
refmprefoc
refsc
refmp
ref
sI
UUI
I
R
1ln minus+
minus
=
α
(4118)
Rs is taken as a constant in the model of this study
Thermal Model of PV From equations (4113) to (4118) it can be noted that the
temperature plays an important role in the PV performance Therefore it is necessary to
have a thermal model for a PV cellmodule In this study a lumped thermal model is
developed for the PV module based on [468] The temperature of the PV module varies
with surrounding temperature irradiance and its output current and voltage and can be
written as
( )aclossPVin
c
PV TTkA
IUΦk
dt
dTC minusminus
timesminus= (4119)
where CPV = the overall heat capacity per unit area of the PV cellmodule [J(˚Cmiddotm2)]
kinPV = transmittance-absorption product of PV cells
kloss = overall heat loss coefficient [W(˚Cmiddotm2)]
Ta = ambient temperature (˚C)
A = effective area of the PV cellmodule (m2)
176
PV Model Development in MATLABSimulink
Based on the mathematical equations discussed before a dynamic model for a PV
module consisting of 153 cells in series has been developed using MATLABSimulink
Figure 450 shows the block diagram of the PV model The input quantities (solar
irradiance Φ and the ambient temperature Ta) together with manufacturer data are used to
calculate the four parameters (4113 -4118) Then based on equation 4112 the output
voltage is obtained numerically The thermal model is used to estimate the PV cell
temperature The two output quantities (PV output voltage U and the PV cell temperature
Tc) and the load current I are fed back to participate in the calculations The model
parameters used in the simulation are given in Table 47 which is based on the values
reported in [468]-[469]
Φ
Figure 450 Block diagram of the PV model built in MATLABSimulink
177
TABLE 47 THE PV MODEL PARAMETERS
ILref (ISCref) 2664 A
αref 5472 V
Rs 1324 Ω
Uocref 8772 V
Umpref 70731 V
Impref 2448 A
Φref 1000 Wm2
Tcref 25 ˚C
CPV 5times104 J(˚Cmiddotm
2)
A 15 m2
kinPV 09
kloss 30 W(˚Cmiddotm2)
Model Performance The model I-U characteristic curves under different irradiances
are given in Figure 451 at 25 ˚C It is noted from the figure that the higher is the
irradiance the larger are the short-circuit current (Isc) and the open-circuit voltage (Uoc)
And obviously the larger will be the maximum power (Pmp) shown in Figure 452 The
maximum power point short-circuit current and open-circuit voltage are also illustrated
in the figures
178
0 10 20 30 40 50 60 70 80 90 1000
05
1
15
2
25
3
Output Voltage (V)
Current (A)
Tc = 25 degC 1000 Wm2
800 Wm2
600 Wm2
400 Wm2
200 Wm2
Uoc
Isc
Figure 451 I-U characteristic curves of the PV model under different irradiances
0 10 20 30 40 50 60 70 80 900
20
40
60
80
100
120
140
160
180
Output Voltage
Output Power (W)
1000 Wm2
800 Wm2
600 Wm2
400 Wm2
200 Wm2
Tc = 25 degC
Pmp
Ump
MaximumPowerPoint
Figure 452 P-U characteristic curves of the PV model under different irradiances
179
Temperature Effect on the Model Performance The effect of the temperature on the
PV model performance is illustrated in Figures 453 and 454 From these two figures it
is noted that the lower the temperature the higher is the maximum power and the larger
the open circuit voltage On the other hand a lower temperature gives a slightly lower
short circuit current
0 10 20 30 40 50 60 70 80 90 1000
05
1
15
2
25
3
Output Voltage (V)
Current (A)
Tc = 50 degC
Φ = 1000 Wm20 degC
25 degC
Figure 453 I-U characteristic curves of the PV model under different temperatures
0 10 20 30 40 50 60 70 80 90 1000
50
100
150
200
Output Voltage
Output Power (W)
Φ = 1000 Wm2
Tc = 50 degC
0 degC
25 degC
Figure 454 P-U characteristic curves of the PV model under different temperatures
180
Maximum Power Point Tracking Control
Though the capital cost for installing a PV array is decreasing due to recent
technology development (see Chapter 1) the initial investment on a PV system is still
very high compared to conventional electricity generation techniques Therefore it is
very natural to desire to draw as much power as possible from a PV array which has
already been installed Maximum power point tracking (MPPT) is one of the techniques
to obtain maximum power from a PV system
Several different MPPT techniques have been proposed in the literature The
techniques summarized in [472] can be classified as (1) Look-up table methods (2)
Perturbation and observation methods and (3) Model-based computational methods Two
major techniques in the ldquoModel-based computational methodsrdquo category are
voltage-based MPPT (VMPPT) and current-based MPPT (CMPPT) techniques Both the
CMPPT and VMPPT methods have been investigated in [472] for matching resistive
loads and DC motor loads A CMPPT method was reported in [473] for matching a DC
motor load In this study a CMPPT method is proposed to obtain maximum power for the
PV array proposed in the AC-coupled hybrid system (see Figure 33 in Chapter 3)
Current-Based Maximum Power Point Tracking The main idea behind the
current-based MPPT is that the current at the maximum power point Imp has a strong
linear relationship with the short circuit current Isc Isc can either be measured on line
under different operation conditions or computed from a validated model Figure 455
shows the curve of Imp vs Isc It can be noted that Imp has a very good linear dependence
on Isc which can be expressed as
181
Imp = kcmppttimesIsc (4120)
where kcmppt is the current factor CMPPT control
0 05 1 15 2 25 3 35 40
05
1
15
2
25
3
35
Short Circuit Current Isc (A)
Imp (A)
Model response
Curve fitting
y = 09245x
Tc = 25 degC
Figure 455 Linear relationship between Isc and Imp under different solar irradiances
75 80 85 9060
62
64
66
68
70
72
Open Circuit Voltage Uoc (V)
Ump (V)
Model response
Curve fittingTc = 25 degC
y = 06659x+ 119
Figure 456 Ump vs Uoc curve under different solar irradiances
182
The VMPPT control is based on the similar idea Figure 456 shows the relationship
between the voltage at the maximum power point Ump and the open circuit voltage Uoc
By comparing Figure 455 and Figure 456 we can see that Figure 455 shows a stronger
linear relationship This is why the CMPPT is used in this study
Control Scheme The control scheme of the CMPPT for the PV system in the
proposed hybrid system is shown Figure 457 The value of Imp calculated form (4120) is
used as the reference signal to control the buck DCDC converter so that the output
current of the PV system matches Imp This reference value is also used to control the
inverter so that the maximum available of power is delivered to the AC bus shown in
Figure 457
Figure 457 CMPPT control scheme
The details on how to control the power electronic devices will be discussed later in
this chapter
183
Simulation Results Simulation studies have been carried out to verify the proposed
CMPPT method For the purpose of simulation the solar irradiance is kept constant at a
value at 600Wm2 for t lt 40 s At t = 40 s the irradiance changes from 600 Wm
2 to 1000
Wm2 shown in Figure 458 This figure also shows the PV output current Ipv and the
reference Imp which is calculated based on (4120) The error between these two currents
is also illustrated in the figure Note that the proposed CMPPT controller works well to
match the PV output current with Imp The corresponding PV output power and the
calculated maximum power curves of the PV system are shown in Figure 459 The figure
also shows that the maximum power point is tracked well with the proposed CMPPT
method
10 20 30 40 50 60 70 800
05
1
15
2
25
Time (s)
Current (A)
Ta = 25 degC
Φ = 600 Wm2
Φ = 1000 Wm2
PV output current Ipv
The error between Ipv and Imp
Imp
Figure 458 Imp and Ipv curves under the CMPPT control
184
10 20 30 40 50 60 70 8060
80
100
120
140
160
180
Time (s)
Power (W)
Ta = 25 degC
Φ = 600 Wm2
Φ = 1000 Wm2
Output Power
Maximum power
Figure 459 PV output power and the maximum power curves
185
Electrolyzer
The fundamentals of operation of electrolyzer have been discussed in Chapter 2
From electrical circuit aspect an electrolyzer can be considered as a voltage-sensitive
nonlinear DC load For a given electrolyzer within its rating range the higher DC
voltage applied the larger is the load current That is by applying a higher DC voltage
we can get more H2 generated Of course more electrical power is consumed at the same
time The model for an electrolyzer stack developed in this study is based on the
empirical I-U equations reported in [468] and [475] described below
U-I Characteristic
The U-I characteristic of an electrolyzer cell can be expressed as [468] [475]
+
+++
++= 1
ln
2
32121
IA
TkTkkkI
A
TrrUU TTT
elecrevcellelec (4121)
where Ueleccell = is the cell terminal voltage (V)
Urev = reversible cell voltage (V)
r1 r2 = parameters for ohmic resistance (Ωmiddotm2 Ωmiddotm
2˚C)
kelec kT1 kT2 kT3 = parameters for overvoltage (V m2A m
2middot˚CA m
2middot˚C
2A)
A = area of cell electrode (m2)
I = electrolyzer current (A)
T = cell temperature (˚C)
The reversible voltage Urev is determined by the Gibbs free energy change of the
electrochemical process as
186
F
GU rev
2
∆minus= (4122)
It is a function of temperature which can be expressed by an empirical equation as
)25(0 minusminus= TkUU revrevrev (4123)
where 0
revU = reversible cell voltage at standard condition (V)
krev = empirical temperature coefficient of reversible voltage (V˚C)
For an electrolyzer stack consisting of nc cells in series the terminal voltage of the
stack can be expressed as
celleleccelec UnU = (4124)
where nc = number of cells in series
Hydrogen Production Rate
According to Faradayrsquo Law [417] [420] the ideal hydrogen production rate of an
electrolyzer stack is given by
F
Inn cH
22 =amp (4125)
where 2Hnamp = hydrogen production rate (mols)
However the actual hydrogen rate is always lower than the above theoretical
maximum value due to parasitic current losses The actual hydrogen production rate can
be obtained as
F
Inn c
FH2
2 η=amp (4126)
where ηF = current efficiency or Faraday efficiency
The current efficiency (ηF) will increase as the current density grows because the
187
percentage of the parasitic current over the total current decreases A higher temperature
will result in a lower resistance value which leads to higher parasitic current and a lower
current efficiency [475] However in high current density regions the effect of
temperature upon current efficiency is small and can be neglected [468] Hence in this
study ηF is considered as function of current density only An empirical formula for ηF is
given in [475] as
( )( ) 22
1
2
f
f
F kAIk
AI
+=η (4127)
where kf1 kf2 = parameters in current efficiency calculation
Thermal Model
The operating temperature of an electrolyzer stack affects its performance
significantly [see (4121)] Therefore it is necessary to have a thermal model for an
electrolyzer stack In this study a lumped thermal model is developed based on the
findings reported in [468] and [475]
coollossgenelec QQQdt
dTC ampampamp minusminus= (4128)
where T = overall electrolyzer temperature (˚C)
Celec = overall heat capacity of the electrolyzer stack (J˚C)
genQamp is the heat power generated inside the electrolyzer stack It can be written as
( )IUUnQ thcelleleccgen minus= amp (4129)
where Uth is the thermal voltage which is expressed as
188
F
STU
F
STG
F
HU revth
222
∆minus=
∆+∆minus=
∆minus= (4130)
lossQamp is the heat power loss It can be determined by
elecT
a
lossR
TTQ
minus=amp (4131)
where Ta = ambient temperature (˚C)
RTelec = equivalent thermal resistance (˚CW)
coolQamp the heat power loss due to cooling can be written as
( )icmocmcmcool TTCQ minus=amp (4132)
where Ccm = overall heat capacity of the flowing cooling medium per second (W˚C)
Tcmo Tcmi = outlet and inlet temperature of the cooling medium (˚C)
Water is used as the cooling medium for the eletrolyzer stack used in this study Tcmo
can be estimated as [468]
minusminusminus+=
cm
HX
icmicmocmC
kTTTT exp1)( (4133)
where kHX = effective heat exchange coefficient for the cooling process It can be
obtained by the following empirical equation [468] [475]
Ihhk convcondHX sdot+= (4134)
where hcond = coefficient related to conductive heat exchange (W˚C)
hconv = coefficient related to convective heat exchange [W(˚CmiddotA)]
189
Electrolyzer Model Implementation in MATLABSimulink
Based on the mathematical equations discussed previously a dynamic model for an
electrolyzer stack consisting of 40 cells in series (50 kW stack) has been developed in
MATLABSimulink Figure 460 shows the block diagram of the electrolyzer model The
input quantities are the applied DC voltage Uelec ambient temperature Ta inlet
temperature of the cooling water Tcm i and the cooling water flow rate ncm The two
output quantities are the hydrogen production rate 2Hnamp and the stack temperature T The
U-I characteristic block [(4121) - (4124)] calculates the electrolyzer current and the
electrolyzer temperature is estimated by the thermal model block (4128-4134) Based on
the calculated electrolyzer current I the current efficiency block (4126-4127) gives the
hydrogen production rate The model parameters are given in Table 48 which is based
on the values reported in [468] and [475]
2Hnamp
Figure 460 Block diagram of the electrolyzer model built in MATLABSimulink
190
TABLE 48 THE ELECTROLYZER MODEL PARAMETERS
r1 805times10-5 Ωmiddotm
2
r2 -25times10-7 Ωmiddotm
2˚C
kelec 0185 V
t1 -1002 m2A
t2 8424 m2middot˚CA
nc 40
krev 193times10-3 V˚C
Celec 6252times105 J˚C
RTelec 0167 ˚CW
A 025 m2
kf1 25times104 Am
2
kf2 096
hcond 70 W˚C
hconv 002 W(˚CmiddotA)
ncm 600 kgh
Ccm (Based on the value of ncm) 69767 W˚C
191
Electrolyzer Model Performance
The U-I characteristics of the electrolyzer model under different cell temperatures are
given in Figure 461 At the same current the higher the operating temperature the lower
the terminal voltage is needed Figure 462 shows the model temperature responses The
ambient temperature and the inlet temperature of the cooling water are set to 25 ˚C for the
simulation study The applied DC voltage starts at 70 V and steps up to 80 V at hour 5
The stack temperature increases from 25 ˚C to 2537 ˚C and stays at that temperature as
long as the applied voltage is 70 V The temperature increases slowly (in approximately 5
hours) to about 302 ˚C when the output voltage jumps to 80 V
0 50 100 150 200 250 300 350 400 450 50060
65
70
75
80
85
90
95
Current (A)
Voltage (V)
T = 25 degC
T = 50 degC
T = 80 degC
Figure 461 U-I characteristics of the electrolyzer model under different temperatures
192
0 1 2 3 4 5 6 7 8 9 1065
70
75
80
85
Time (hour)
Voltage (V)
0 1 2 3 4 5 6 7 8 9 1025
30
35
Stack Temperature (degC)
Voltage
Temperature
Ta = Tcmi = 25 degC
Figure 462 Temperature response of the model
193
Power Electronic Interfacing Circuits
Power electronic (PE) interfacing circuits also called power conditioning circuits are
necessary for a hybrid energy system like the one proposed in Chapter 3 (see Figure 33)
In this section the electrical circuit diagrams state-space models and effective
average-models (for long-time simulation studies) for the main PE interfacing circuits in
the proposed hybrid energy system are discussed They are ACDC rectifiers DCDC
converters DCAC inverters
A detailed model for a PE device together with the control switching signals will
dramatically decrease the simulation speed using MATLABSimulink The detailed
models for PE devices such as those given in the SimPowerSystems block-set are not
suitable for long time simulation studies Effective average-models for PE devices will be
developed in this section which help improve the simulation speed significantly and at
the same time keep the desirable accuracy
ACDC Rectifiers
Circuit Topologies Basically there are two types of ACDC rectifiers
controllableuncontrollable rectifiers Uncontrollable rectifiers are normally referred to
diode (or diode bridge) rectifiers Figure 463 shows a typical three-phase full diode
bridge rectifier [441]
194
Figure 463 Three-phase full diode bridge rectifier
If Ls = 0 in the above figure the average value of the output DC voltage Vdc is given
as [441]
LLdc VV 23
π= (4135)
where VLL is the AC source line-line RMS voltage
The quality of the output DC voltage is fairly good The voltage ripple is within plusmn 5
However the input AC current ia for example is distorted The AC side inductor Ls can
be increased to reduce the current distortion But this will cause extra voltage drop across
the inductor Another way is to use a Y-Y and a Y-∆ connection transformer to form a
12-diode bridge rectifier as shown in Figure 464 There is a 30˚ phase shift between the
two transformer outputs which reduces the transition period from 60˚ to 30˚ in one (360˚)
period The average value of the DC output voltage now is
195
LLdc VV 26
π= (4136)
where VLL is the line-line RMS voltage of the transformersrsquo output
The output DC voltage ripple now is reduced to within plusmn 115 and the harmonics of
the AC side current are much reduced The total harmonic distortion (THD) of a 12-pulse
rectifier is typically 12 with the 11th and 13th harmonics dominant while the THD of a
6-pulse rectifier is about 30 with the 5th and 7th harmonics dominant [441] [476]
Figure 464 Three-phase 12-diode bridge rectifier with a Y-Y and a Y-∆ transformer
Based on the same principle a 24-diode rectifier can be built using zig-zag
transformer group [476] But it is not used commonly in low power rating applications
Controllable rectifiers are normally firing angle controlled thyristor rectifiers and
pulse width modulated (PWM) rectifiers A PWM rectifier has the same circuit topology
as a PWM inverter which will be discussed later in this section It is just the same circuit
196
working at a different operation modes inverter mode vs rectifier mode Therefore only
the thyristor rectifier is discussed here
A thyristor can work just like a diode with the exception that it starts to conduct
when it is not only forward biased but also its gate receives a positive current pulse and
it continues to be conducting as long as it is still forward biased Thyristors can be used in
Figure 463 and 474 to replace the diodes Figure 465 shows a 6-pulse thyristor rectifier
The output DC voltage can be regulated by controlling the firing angles of thyristors The
firing angle α shown in Figure 465 is the angular delay between the time when a
thyristor is forward biased and the time when a positive current pulse is applied to its gate
For a 6-pulse thyristor rectifier the output DC voltage is [441]
)cos(23
απ LLdc VV = (4137)
where α = firing angle
If cos(α) is taken as the control variable it is noted from the above equation that the
output voltage of a thyristor rectifier is proportional to the control input
197
α
Figure 465 A 6-pulse thyristor rectifier
Simplified Model for Controllable Rectifiers Figure 466 shows the block diagram
of the simplified ideal model for controllable three phase rectifiers This model is
developed for long time simulation studies The ldquoline-line voltage peak valuerdquo block
calculates the peak value of the AC line-line voltage LLV2 The input quantity g which
can be considered as cos(α) is the control variable to regulate the output DC voltage The
output DC voltage is calculated based on (4137) For 6-pulse rectifiers gain kdc is 3π
Then the signal Edc is fed to control a controlled voltage source which actually is the DC
output of the model The series resistor Rs is used to model the power and voltage losses
within a real rectifier The ldquoP Q Calculationrdquo block calculates the amount of the real and
reactive power consumed at the AC side based on the DC side real power and the input
198
quantity power angle θ shown in Figure 466 The ldquodynamic loadrdquo block is a built-in
model in Simulink which consumes the real and reactive power assigned by its P amp Q
inputs
Figure 466 Block diagram of the simplified model for 3-phase controllable rectifiers
Figures 467 and 468 compare the voltage and current responses of the simplified
ideal rectifier model with the detailed rectifier models a 6-pulse model and a 12-pulse
model with the same AC source and the same DC load Figure 467 shows that the
average output DC voltage of the ideal model is slightly higher than those of the detailed
rectifier models Figure 468 shows the AC side phase current of the different models It
is noted that the AC current is distorted for the 6-pulse rectifier model However the
harmonic is much reduced for the 12-pulse rectifier model and the response of this
rectifier model is very close to that of the ideal rectifier model The simplified ideal
199
controllable rectifier model shown in Figure 466 is used in the proposed hybrid energy
system It can improve the simulation speed and at the same time keep the desired
accuracy
032 033 034 035 036265
270
275
Time (s)
Output DC Voltage (V) Ideal rectifier model
6-pulse thyristorrectifier model
12-pulse thyristorrectifier model
Figure 467 DC output voltages of the different rectifier models
032 033 034 035 036
-30
-20
-10
0
10
20
30
Time (s)
AC side phase current (A)
Idealrectifiermodel
6-pulsethyristorrectifiermodel
12-pulsethyristorrectifiermodel
Figure 468 AC side phase current of the different rectifier models
200
DCDC Converters
There are many types of DCDC converters In this section only typical boost
converters and buck converters are discussed
Circuit Topologies Figure 469 shows the circuit diagram of a boost DCDC
converter (inside the rectangle) The output voltage regulation feedback is also given in
the figure At steady-state the average value of the output voltage is given as
)1(
_
_d
VV
indd
outdd minus= (4138)
where d is the duty ratio of the switching pulse
Since 10 ltle d the output voltage is always higher than the input voltage5 That is
why the circuit (in Figure 469) is called a boost DCDC converter The controller for the
converter is to regulate the DC bus voltage within a desirable range The output voltage is
measured and compared with the reference value The error signal is processed through
the PWM controller which can be a simple PI controller The output of the controller is
used to generate a PWM pulse with the right duty ratio so that the output voltage follows
the reference value
5 When d=1 the input is short circuited and the circuit will not work This situation should be avoided d
normally is less than 085 [476]
201
Figure 469 Boost DCDC converter
Figure 470 Buck DCDC converter
A buck DCDC converter is shown in Figure 470 At steady-state the average value
of the output voltage is given as
202
inddoutdd dVV __ = (4139)
Since 10 lele d the output voltage of a buck converter is always lower than its input
voltage In contrast to a boost converter a buck converter is a step-down DCDC
converter Its output voltage can also be regulated by controlling the duty ratio (d) of the
switching signals The voltage regulation feedback loop is also shown in Figure 470
State-space Models Based on the State-space Averaging Technique In order to
apply classical control analysis and design methods (such as Nyquist criterion Bode plots
and root loci analysis) in converter controls state-space small-signal models for the
above boost and buck converters are needed and are discussed in this section These
models are based on the state-space averaging technique developed by Middlebrook Cuacutek
and their colleagues [477]
1) State-space model for boost DCDC converters
In Figure 469 take ddLix =1 and Cddvx =2 as state variables Let xXx ~+=
dDd~
+= inddinddindd vVv ___~+= and outddoutddoutdd vVv ___
~+= ldquo~rdquo here is used to
denote small perturbation signals and state variable X denotes the system operating point
When the switch Sdd is on and diode Ddd is off the state-space representation of the
main circuit can be written as
xCv
vBxAx
T
outdd
indd
1_
_11
=
+=amp (4140)
where
minus=
ddRC
A 10
00
1
=
0
11
ddLB and ]10[1 =TC
203
When switch Sdd is off and diode Ddd is on the state-space equation of the circuit
turns out to be
xCv
vBxAx
T
outdd
indd
2_
_22
=
+=amp (4141)
where
minus
minus
=
dddd
dd
RCC
LA
11
10
2
=
0
12
ddLB and ]10[2 =TC
Therefore the average state-space model of the main circuit at the operating point is
xCv
BvAxx
T
outdd
indd
=
+=
_
_amp
(4142)
where
minusminus
minusminus
=
dddd
dd
RCC
d
L
d
A11
)1(0
===
0
121
LBBB and ]10[21 === TTT CCC
Then the small signal model for the boost DCDC converter can be obtained as
xCv
vBdBxAx
T
outdd
inddvdd
~~
~~~~
_
_
=
++=amp (4143)
where
minusminus
minusminus
=
dddd
ddd
RCC
D
L
D
A11
)1(0
minus=
dd
dd
dCX
LXB
1
2
=
0
1 dd
v
LB X1 and X2 are the steady
state values of x1 and x2 respectively
Using Eq (4143) and only considering the perturbation of duty ratio d~ ( inddv _~ =0)
204
the transfer function )(
~)(~
)(_
sd
svsT
outdd
vd = is obtained as
[ ]
minus+minus
minus++
=minus= minus
dddddd
dddddd
dd
T
vdCL
XD
C
sX
CL
D
RCss
BASICsT 21
2
1 )1(
)1()
1(
1)( (4144)
2) State-Space model for buck DCDC converters
Similar to the procedure discussed in the previous part a small-signal state-space
model of a buck converter can be obtained which has been reported in [441] and [476]
as
xCv
dBxAx
T
boutdd
bb
=
+=
_
amp
(4145)
where
=
Cdd
ddL
v
ix
minus
minus=
dddd
ddb
RCC
LA
11
10
=
0
_
dd
indd
b L
V
B ]10[=T
bC
The small signal model can be obtained as
xCv
dBxAx
T
boutdd
bb
~~
~~~~
_ =
+=amp (4146)
where
=
Cdd
ddL
v
ix ~
~~ and
=
0
~ _ ddindd
b
LVB
Similarly the transfer function for the output voltage over duty ratio can be obtained
++
==
dddddd
dddd
inddoutdd
p
CLRC
ssCL
V
sd
svsT
1)(~
)(~
)(2
__ (4147)
205
Averaged Models for DCDC Converters Averaged models for boost and buck
DCDC converters suitable for long time simulation studies are given in this part These
models simulate the DCDC converter transient behavior in large scale rather than the
detailed cycle-to-cycle variations of values of voltages and currents The models
discussed here are based on the models reported in [476]
1) Averaged model for boost DCDC converters
Lddid times
outddVd _times
Figure 471 Averaged model for boost DCDC converters
Comparing the circuit diagram of boost converter in Figure 469 and its averaged
model shown in Figure 471 we can see that the power electronic switch and diode are
replaced by the combination of controlled current and voltage sources in the averaged
model This gives the same performance as the detailed circuit model at large time scale
Figures 472 and 473 show the simulation results of the averaged model and the detailed
circuit model under a load change It is noted from these two figures that the averaged
model can simulate the converter behavior precisely at large time scale with reasonable
accuracy
206
008 009 01 011 012 013 014 015 016120
140
160
180
200
220
240Output Voltage (V)
008 009 01 011 012 013 014 015 016150
200
250
300
350
400
450
Time (s)
Inductor Current (A)
Output Voltage
Inductor Current
Figure 472 Simulation result of the averaged model for boost DCDC converter
008 009 01 011 012 013 014 015 016120
140
160
180
200
220
240
Output Voltage (V)
008 009 01 011 012 013 014 015 016150
200
250
300
350
400
450
Time (s)
Inductor Current (A)
Inductor Current
Output Voltage
Figure 473 Simulation result of the detailed model for boost DCDC converter
207
2) Averaged model for buck DCDC converters
Lddid times
inddVd _times
Figure 474 Averaged model for buck DCDC converters
Figure 474 shows the averaged model for buck converters Simulation results shown
in Figures 475 and 476 illustrate the effectiveness of the averaged model for buck
DCDC converters
008 009 01 011 012 013 01430
40
50
60
Output Voltage (V)
008 009 01 011 012 013 0140
40
80
120
Time (s)
Inductor Current (A)
Inductor Current
Output Voltage
Figure 475 Simulation result of the averaged model for buck DCDC converter
208
008 009 01 011 012 013 01430
40
50
60Output Voltage (V)
008 009 01 011 012 013 0140
40
80
120
Time (s)
Inductor Current (A)
Output Voltage
Inductor Current
Figure 476 Simulation result of the detailed model for buck DCDC converter
DCAC Inverters
Circuit Topology A 3-phase 6-switch DCAC PWM voltage source inverter is used
to convert the power from DC to AC Figure 477 shows the main circuit of a 3-phase
voltage source inverter (VSI) which is connected to the AC bus or utility grid through
LC filters and coupling inductors
State-Space Model For deducing convenience the neutral point N of the AC
system is chosen as the common potential reference point For the purpose of simplicity
only the inverter under balanced loads and without a neutral line (used in this dissertation)
is discussed Define the following switching functions
209
minus=
minus
+
OFFS
ONSd
a
a
1
1
1
minus=
minus
+
OFFS
ONSd
b
b
1
1
2 (4148)
minus=
minus
+
OFFS
ONSd
c
c
1
1
3
Figure 477 3-phase DCAC voltage source inverter
van vbn and vcn (the inverter output voltages between each phase and its imaginary
neutral point n) can be expressed as
=
=
=
dccn
dcbn
dcan
Vd
v
Vd
v
Vd
v
2
2
2
3
2
1
(4149)
where Vdc is the DC bus voltage
The output phase potentials of the inverter va vb and vc can be obtained as
210
+=
+=
+=
ncnc
nbnb
nana
vvv
vvv
vvv
(4150)
where vn is the voltage between the point n and the common reference neutral point N
Since 0=++ fcfbfa iii and 0=++ CBA eee vn is obtained as [478]-[479]
sum=
minus=3
1
6 k
k
dc
n dV
v (4151)
For the circuit shown in Figure 477 the following dynamic equations can be
obtained
++=
++=
++=
scfcf
fc
fc
sbfbf
fb
fb
safaf
fa
fa
viRdt
diLv
viRdt
diLv
viRdt
diLv
(4152)
minus+
minus+=
minus+
minus+=
minus+
minus+=
dt
vvdC
dt
vvdCii
dt
vvdC
dt
vvdCii
dt
vvdC
dt
vvdCii
sbscf
sascfscfc
scsbf
sasbfsbfb
scsaf
sbsafsafa
)()(
)()(
)()(
(4153)
minus=+
minus=+
minus=+
Cscsc
sscs
Bsbsb
ssbs
Asa
sa
ssas
evdt
diLiR
evdt
diLiR
evdt
diLiR
(4154)
Writing the above equations into the state-space form
abcabcabcabcabc UBXAX +=amp (4155)
211
where [ ]Tscsbsascsbsafcfbfaabc iiivvviiiX = [ ]TCBAdcabc eeeVU =
minus
minus
minus
minus
minus
minus
minusminus
minusminus
minusminus
=
s
s
s
s
s
s
s
s
s
ff
ff
ff
ff
f
ff
f
ff
f
abc
L
R
L
L
R
L
L
R
L
CC
CC
CC
LL
R
LL
R
LL
R
A
001
00000
0001
0000
00001
000
3
100000
3
100
03
100000
3
10
003
100000
3
1
0001
0000
00001
000
000001
00
and
minus
minus
minus
minus
minus
minus
=
sum
sum
sum
=
=
=
s
s
s
f
k
k
f
k
k
f
k
k
abc
L
L
L
Ldd
Ldd
Ldd
B
1000
01
00
001
0
0000
0000
0000
0006
1
2
0006
1
2
0006
1
2
3
1
3
3
1
2
3
1
1
212
dq Representation of the State-Space Model The dq transformation transfers a
stationary 3-coordinate (abc) system to a rotating 2-coordinate (dq) system The dq
signals can be used to achieve zero tracking error control [478] Due to this merit the dq
transformation has been widely used in PWM converter and rotating machine control
[462] [478] [480]
Using the dq transformation explained in [462] (see Appendix A) the system
state-space equation given in (4155) can be represented in the rotating dq frame as
dqdqdqdqdq UBXAX +=amp (4156)
where
[ ]Tsqsdsqsddqdddq iivviiX = [ ]Tqddcdq eeVU =
=
dc
db
da
dqabc
dq
dd
i
i
i
Ti
i
=
sc
sb
sa
dqabc
sq
sd
v
v
v
Tv
v and
=
C
B
A
dqabc
q
d
e
e
e
Te
e
minusminus
minus
minusminus
minus
minusminusminus
minusminus
=
s
s
s
s
s
s
ff
ff
ff
f
ff
f
dq
L
R
L
L
R
L
CC
CC
LL
R
LL
R
A
ω
ω
ω
ω
ω
ω
1000
01
00
3
100
3
10
03
100
3
1
001
0
0001
minus
minus
=
100
010
000
000
00)(
00)(
3
2
12
3
2
11
f
f
dq
L
dddtf
L
dddtf
B
f1 and f2 are obtained as
213
minus++
minusminus+
minus
=
sum
sumsum
=
==
3
1
3
3
1
2
3
1
1
3
2
11
3
1)
3
2sin(
3
1)
3
2sin(
3
1)sin(
3
1
)(
k
k
k
k
k
k
ddt
ddtddt
dddtf
πω
πωω
minus++
minusminus+
minus
=
sum
sumsum
=
==
3
1
3
3
1
2
3
1
1
3
2
12
3
1)
3
2cos(
3
1)
3
2cos(
3
1)cos(
3
1
)(
k
k
k
k
k
k
ddt
ddtddt
dddtf
πω
πωω
Tabcdq is the abcdq transformation matrix The methodology for developing the
abcdq transformation is explained in [462] (see Appendix A)
214
Ideal Model for Three-phase VSI Figure 478 shows the ideal model for a
three-phase VSI It is not a detailed model with all the power electronic switches and
switching signals it is an idealized model used for long time simulation studies The load
current of the input DC voltage source (Idc) is determined by the power consumed at the
AC side The other three input quantities are the desired output AC frequency f AC
voltage amplitude index (similar to the modulation index in a real VSI control) m and the
initial phase of the three-phase AC output voltages 0φ The ldquoabc signal formationrdquo block
gives the base signals for the three phases va(t) vb(t) and vc(t)
++=
++=
+=
)342sin()(
)322sin()(
)2sin()(
0
0
0
φππφππ
φπ
ftmtv
ftmtv
ftmtv
c
b
a
(4157)
The output voltage values Va(t) Vb(t) and Vc(t) are calculated by multiplying the
base signal values by the possible peak of the output AC which is 05Vdc For example
Va(t) = 05Vdctimesva(t) Then Va(t) Vb(t) and Vc(t) are used to control the three controlled
voltage sources which are the AC output voltages of the inverter model The AC power
is calculated through the ldquoPower Calculationrdquo block as
)()()()()()( tVtItVtItVtIP ccbbaaac times+times+times= (4158)
For the purpose of comparison a 208 V three-phase VSI is simulated to supply 100
kW to a load both by the ideal model shown in Figure 478 and the switched model given
in Figure 477 Figure 479 shows the output AC phase voltage of the two models It is
noted that though there are harmonics in voltage from the switched model its output
voltage waveform is very close to the output from the ideal model when a properly
215
designed filter is applied to the system Figure 480 shows the output power to the load
from the two models We can see that the ideal model output is ideal delivering a
constant power of 100 kW On the other hand a more practical and detailed output power
curve (with ripples) is obtained from the switched model Nevertheless the ideal model is
capable of simulating a VSI with good accuracy at large time scale
0φ
Figure 478 Ideal model for three-phase VSI
216
16 161 162 163 164
-150
-100
-50
0
50
100
150
Time (s)
AC phase voltage (V)
Figure 479 AC phase output voltages of the ideal VSI model and the switched VSI
model
16 162 164 166 168 170
50
100
150
200
Time (s)
Output Power (kW)
Switched Model
Ideal Model
Figure 480 Output power of the ideal VSI model and the switched VSI model
217
Battery Model
A validated electrical circuit model for lead-acid batteries shown in Figure 481 was
reported in [481] The diodes in the model are all ideal and just used to select different
resistances for charging and discharging states The model parameters (capacitances and
resistances) defined in Figure 481 are functions of battery current temperature and state
of charge (SOC) [481] [482] However within the voltage range (100plusmn5) there is not
a big difference between the charge and discharge resistances [481] For the purpose of
analysis these component values in the model are considered constant within the100plusmn5
voltage range in this study Then the model shown in Figure 481 can be simplified into
the circuit model given in Figure 482
Cb= battery capacitance Rp= self-discharge resistance or insulation resistance
R2c= internal resistance for charge R2d= internal resistance for discharge
R1c= overvoltage resistance for charge R1d= overvoltage resistance for discharge
C1= overvoltage capacitance
Figure 481 Equivalent circuit model for battery reported in [481]
218
Figure 482 Simplified circuit model for lead-acid batteries
Models for Accessories
Gas Compressor
A gas compressor can be modeled by considering the compression process as a
two-stage polytropic compression which can be described as [422]
CVP m
ii = (4159)
where Pi Vi = the pressure and voltage at stage i (1 2)
m = polytropic exponent
C = constant
Based on the above equation the power needed to compress a gas at pressure P1 to
pressure P2 with the flow rate gasnamp can be obtained as
comp
m
m
x
gascompP
P
m
mRTnP
η1
11
2
1
2
minus
minus=
minus
amp (4160)
where Pcomp = power consumed (W)
gasnamp = gas flow rate (mols)
219
R = gas constant 83144 J(molmiddotK)
T = gas temperature (K)
P2 = exit pressure (Pa)
21PPPx = intermediate pressure (Pa)
P1 = inlet pressure (Pa)
ηcomp = overall efficiency of the compressor
High Pressure H2 Storage Tank
For H2 in the high pressure storage tank shown in Figure 483 the ideal gas equation
does not accurately describe the relation between P V and T a modified equation of state
should be used The Beattie-Bridgeman equation has been successful in fitting the
measured values of pressure volume and temperature in a high-pressure gas storage tank
with good accuracy [422] This modified state equation can be written as
innamp outnamp
Figure 483 Pressured H2 storage tank
2
2
0
032
21
11V
nV
anA
V
bnB
n
V
VT
cn
V
RTnP
minusminus
minus+
minus= (4161)
where P = pressure of hydrogen in the tank (atm)
V = Volume of the tank (liter)
220
T = temperature of H2 (K)
n = number of moles of H2 in the tank
R = Gas constant 008206 atmmiddotliter(molmiddotK)
A0 B0 a b c are constants for certain type of gas Their values for H2 are given
in Table 49
The change of mole number of gas (H2) in the tank is governed by
outin nndt
dnampamp minus= (4162)
TABLE 49 CONSTANTS OF BEATTIE-BRIDGEMAN EQUATION OF STATE FOR H2 [422]
A0 01975 atmmiddotliter2mol
2
B0 002096 litermol
a -000506 litermol
b -004359 litermol
c 00504times104 litermiddotK3mol
Gas Pressure Regulator
Figure 484 shows a schematic diagram of a commonly used gas pressure regulator
[483] Its function is to keep the output pressure Po constant at a desired value (Pref)
under changes of the gas flow rates qo The pressure regulation is achieved by the
deformation of the diaphragm Suppose there is a reduction in Po which will reduce the
pressure against the bottom of the diaphragm This causes the spring force to push
downward to increase the valve opening in the direction axis x Therefore the valve flow
221
is increased and as a result the output pressure Po is raised back toward the reference
value The system can be modeled by the following equations [483]
( )( )oicxi PPkxkq minus+= (4163)
where qi = input flow rate (mols)
kx kc = constants used in calculating fluid resistanceadmittance [mol(Pamiddotsmiddotm)
mol(Pamiddots)]
Figure 484 Gas pressure regulator
The net flow entering the volume below the diaphragm is
( )( ) ooicxoinet qPPkxkqqq minusminus+=minus= (4164)
Normally the diaphragm deformation is small hence the volume V can be considered
constant The dynamic state equation can be written as
ognet PCq amp= (4165)
where Cg = VRT The output pressure Po can be expressed as
A
xkPP s
refo minus= (4166)
where ks = spring constant (Nm)
A = diaphragm area (m2)
Figure 485 shows the model performance under output flow variations and the
222
variations in reference pressure The model is adjusted to keep the output pressure at the
reference value at the flow rate of 01 mols The reference pressure steps up from 2 atm
to 3 atm at 10 s The figure shows that the output pressure follows the reference value
very well It is noted from the figure that the output pressure drops a little bit (from 2 atm
to about 198 atm) when the output flow rate jumps up to 02 mols at 2 s The output
pressure comes back to its preset value (2 atm) when the output flow rate drops back to
01 mols at 6 s
2 4 6 8 10 12 14 1615
2
25
3
35
Pressure (atm)
2 4 6 8 10 12 14 160
01
02
Time (s)
Flow rate (mols)
Output flow rate qo
Output pressure Po
Pref
Figure 485 Performance of the model for gas pressure regulators
223
Summary
In this chapter the model development for the components of the proposed hybrid
alternative energy system is discussed These components are fuel cells (PEMFCs and
SOFCs) variable speed wind energy conversion unit solar power generation unit
electrolyzers power electronic interfacing devices battery bank and accessories
including gas compressor high-pressure H2 storage tank and gas pressure regulator
Performance evaluation of these models is also discussed in this chapter The models will
be used in Chapters 5 and 6 to investigate grid-connected and stand-alone fuel cell power
generation systems and in Chapter 7 for the study of hybrid energy systems
224
REFERENCES
[41] J C Amphlett R M Baumert R F Mann B A Peppley and P R Roberge
ldquoPerformance Modeling of the Ballard Mark IV Solid Polymer Electrolyte Fuel
Cell I Mechanistic Model Developmentrdquo Journal of the Electrochemical Society
Vol 142 No 1 pp 1-8 Jan 1995
[42] J C Amphlett R M Baumert R F Mann B A Peppley and P R Roberge
ldquoPerformance Modeling of the Ballard Mark IV Solid Polymer Electrolyte Fuel
Cell II Empirical Model Developmentrdquo Journal of the Electrochemical Society
Vol 142 No 1 pp 9-15 Jan 1995
[43] R Cownden M Nahon M A Rosen ldquoModeling and Analysis of a Solid Polymer
Fuel Cell System for Transportation Applicationsrdquo International Journal of
Hydrogen Energy Vol 26 No 6 pp 615-623 June 2001
[44] Charles E Chamberlin ldquoModeling of Proton Exchange Membrane Fuel Cell
Performance with an Empirical Equationrdquo Journal of the Electrochemical Society
Vol 142 No 8 pp 2670-2674 August 1995
[45] Andrew Rowe Xianguo Li ldquoMathematical Modeling of Proton Exchange
Membrane Fuel Cellsrdquo Journal of Power Sources Vol 102 No 1-2 pp82-96
Dec 2001
[46] D Bevers M Woumlhr ldquoSimulation of a Polymer Electrolyte Fuel Cell Electroderdquo
Journal of Applied Electrochemistry Vol27 No 11 pp 1254-1264 Nov 1997
[47] G Maggio V Recupero L Pino ldquoModeling Polymer Electrolyte Fuel Cells An
Innovative Approachrdquo Journal of Power Sources Vol 101 No 2 pp275-286 Oct
2001
[48] J C Amphlett R F Mann B A Peppley P R Roberge and A Rodrigues ldquoA
Model Predicting Transient Responses of Proton Exchange Membrane Fuel Cellsrdquo Journal of Power Sources Vol 61 No 1-2 pp 183-188 July-Aug 1996
[49] J Hamelin K Agbossou A Laperriegravere F Laurencelle and T K Bose ldquoDynamic
Behavior of a PEM Fuel Cell Stack for Stationary Applicationsrdquo International
Journal of Hydrogen Energy Vol 26 No 6 pp 625-629 June 2001
[410] M Woumlhr K Bolwin W Schnurnberger M Fischer W Neubrand and G
Eigenberger ldquoDynamic Modeling and Simulation of a Polymer Membrane Fuel
Cell Including Mass Transport Limitationrdquo International Journal of Hydrogen
Energy Vol 23 No 3 pp 213-218 March 1998
225
[411] Hubertus PLH van Bussel Frans GH Koene and Ronald KAM Mallant
ldquoDynamic Model of Solid Polymer Fuel Cell Water Managementrdquo Journal of
Power Sources Vol 71 No 1-2 pp 218-222 March 1998
[412] M Wang M H Nehrir ldquoFuel Cell Modeling and Fuzzy Logic-Based Voltage
Controlrdquo International Journal of Renewable Energy Engineering Vol 3 No 2
August 2001
[413] Michael D Lukas Kwang Y Lee Hossein Ghezel-Ayagh ldquoPerformance Implications of Rapid Load Changes in Carbonate Fuel Cell Systemsrdquo
Proceedings 2001 IEEE Power Engineering Society Winter Meeting Vol 3 pp
979-984 2001
[414] Robert Lasseter ldquoDynamic Models for Micro-turbines and Fuel Cellsrdquo
Proceedings 2001 IEEE Power Engineering Society Summer Meeting Vol 2 pp 761-766 2001
[415] Padmanabhan Srinivasan Ali Feliachi John Ed Sneckenberger ldquoProton Exchange
Membrane Fuel Cell Dynamic Model for Distributed Generation Control
Purposesrdquo Proceedings 34th North American Power Symposium pp 393-398
Oct 2002 Tempe Arizona
[416] Pariz Famouri and Randall S Gemmen ldquoElectrochemical Circuit Model of a PEM
Fuel Cellrdquo Proceedings 2003 IEEE Power Engineering Society Summer Meeting
0-7803-7990-X03 July 2003 Toronto Canada
[417] James Larminie and Andrew Dicks Fuel Cell Systems Explained John Wiley amp
Sons Ltd 2001
[418] Fuel Cell Handbook (Sixth Edition) EGampG Services Inc Science Applications
International Corporation DOE Office of Fossil Energy National Energy
Technology Lab Nov 2002
[419] JA Smith MH Nehrir V Gerez and SR Shaw ldquoA Broad Look at the Workings
Types and Applications of Fuel Cellsrdquo Proceedings 2002 IEEE Power
Engineering Society Summer Meeting Vol 1 pp 70-75 July 2002 Chicago IL
[420] G Kortum Treatise on Electrochemistry (2nd Edition) Elsevier Publishing
Company 1965
[421] A Schneuwly M Baumlrtschi V Hermann G Sartorelli R Gallay and R Koetz
ldquoBOOSTCAP Double-Layer Capacitors for Peak Power Automotive Applicationsrdquo Proceedings the Second International ADVANCED
AUTOMOTIVE BATTERY Conference (AABC) Las Vegas Nevada February
2002